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9042 



Bureau of Mines Information Circular/1985 




Mine Subsidence Control 

Proceedings: Bureau of Mines Technology 
Transfer Seminar, Pittsburgh, PA, 
September 19, 1985 



Compiled by Staff, Bureau of Mines 




UNITED STATES DEPARTMENT OF THE INTERIOR 



75 

'W/NES 75TH AV*^ 






Information Circular 9042 



Mine Subsidence Control 

Proceedings: Bureau of Mines Technology 
Transfer Seminar, Pittsburgh, PA, 
September 19, 1985 



Compiled by Staff, Bureau of Mines 




l cCf j g5-(oOOZ[t 



UNITED STATES DEPARTMENT OF THE INTERIOR 
Donald Paul Hodel, Secretary 

BUREAU OF MINES 
Robert C. Horton, Director 



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PREFACE 



$( This Information Circular summarizes recent Bureau of Mines research 

aimed at improving technology for predicting and controlling mine sub- 
sidence. The four papers contained in this publication constitute a 
large portion, but not all, of the research being performed by the Bu- 
reau in this area. 

The papers were presented at a technology transfer seminar on mine 
subsidence control in September 1985. Technology transfer seminars are 
sponsored frequently by the Bureau of Mines to direct the mineral in- 
dustry's attention to research results that may be useful and helpful 
in solving problems. Those desiring more information about Bureau re- 
search programs should contact the Bureau of Mines, Branch of Technol- 
ogy Transfer, 2401 E St., NW, Washington, DC 20241. 



CONTENTS 



111 



Page 



Preface i 

Abstract 1 

Introduction 1 

Longwall mine subsidence surveying — an engineering technology comparison, 

by Gary W. Krantz and John C. LaScola 2 

Short-term effects of longwall mining on shallow water sources, by Noel N. 

Moebs and Timothy M. Barton 13 

Comparison of the subsidence over two different longwall panels, by Paul W. 

Jeran and Timothy M. Barton 25 

Precalculation of subsidence over longwall panels in the northern Appalachian 

coal region, by Vladimir Adamek and Paul W. Jeran 34 





UNIT OF 


MEASURE 


ABBREVIATIONS USED 


IN THIS REPORT 


cm 


centimeter 




mm 


millimeter 


deg 


degree 




mm/m 


millimeter per meter 


ft 


foot 




ym 


micrometer 


ft/d 


foot per day 




pmho/cm 


micrometer per centimeter 


gpm 


gallon per minute 


pet 


percent 


h 


hour 




ppm 


part per million 


in 


inch 




V ac 


volt, alternating current 


km 


kilometer 




V dc 


volt, direct current 


min 


minute (time) 




W 


watt 



MINE SUBSIDENCE CONTROL 

Proceedings: Bureau of Mines Technology Transfer Seminar, 
Pittsburgh, PA, September 19, 1985 

Compiled by Staff, Bureau of Mines 



ABSTRACT 

This publication contains four papers presented at a seminar on mine 
subsidence control held in Pittsburgh, PA, on September 19, 1985. The 
seminar was designed to keep the mineral industry informed of new tech- 
nology developed by the Bureau of Mines that permits reliable and accu- 
rate prediction of mine subsidence. The papers describe actual field 
studies undertaken by the Bureau to monitor surface subsidence over 
longwall panels. Topics discussed include the efects of subsidence on 
water table levels, the development of subsidence precalculation meth- 
odology suitable for use with the specific lithological conditions of 
the Pittsburgh coalbed, an engineering comparison of technologies used 
in surveying for longwall mine subsidence, and a comparison of the pro- 
cess of subsidence over two different longwall panels. 

INTRODUCTION 

To minimize damage caused by mining-related subsidence, a better un- 
derstanding of the relationship between underground mining and subse- 
quent surface movement is needed. Such an understanding, coupled with 
information gathered while researching this relationship, can be used 
advantageously by mine operators to predict when and where subsidence 
will occur. Mine subsidence prediction methods have been developed by 
European countries, but these methods are tailored to the mining and 
geologic conditions of those countries — conditions that often differ 
greatly from those of the United States. To fill the existing subsi- 
dence information and technology voids, the Bureau of Mines conducted 
in-depth research to develop techniques that permit accurate prediction 
of surface ground movements over underground mines. The investigation 
entailed an extensive data gathering effort to properly characterize 
the extent and nature of subsidence under various geologic conditions. 
Results of this research are presented in this Information Circular 
through four papers presented at a Technology Transfer Seminar on Mine 
Subsidence Control on September 19, 1985, in Pittsburgh, PA. 



LONGWALL MINE SUBSIDENCE SURVEYING—AN ENGINEERING TECHNOLOGY COMPARISON 
By Gary W. Krantz 1 and John C. LaScola^ 

ABSTRACT 



A typical longwall mine subsidence sur- 
vey monitoring grid was installed at the 
Bureau of Mines. Conventional and high- 
technology surveying systems, including 
an electronic distance meter-theodolite- 
level, (EDM-theodolite) , an automatic 
recording infrared laser tacheometer, a 
global positioning system satellite 



surveyor, aerial photography (photogram- 
metry) , and a prototype inertial surveyor 
were developed over the grid during a 
1-month period. A statistical analysis 
indicates that the average three-dimen- 
sional displacements from the base (EDM- 
theodolite) for both the tacheometer and 
photogrammetry were almost identical. 



INTRODUCTION 



This investigation evaluates and com- 
pares five surveying methodologies 
available for use in surface longwall 
subsidence monitoring. They include EDM- 
theodolite, tacheometer, and photogram- 
metry surveying. Inertial surveying 
systems are discussed, but an in-depth 
evaluation was impossible owing to on- 
site system failure. 



Geodetic survey work is conducted to 
establish time-based def ormational char- 
acteristics of the ground surface as the 
longwall mine face advances beneath. 
Surface monuments installed above the 
mine panel must be accurately and repeti- 
tively measured to determine the dynamic 
vertical and horizontal movements. 



ACKNOWLEDGMENTS 



The authors would like to acknowledge 
the assistance provided by the U.S. Army, 
Corps of Engineers, Huntington, WV , Dis- 
trict and Ft. Belvoir, VA, Engineering 
Topographic Laboratory; Jan Stenstroem 
of Carl Zeiss, Inc., Thornwood, NY; 



Geo-Hydro Inc., of Rockville, MD; the 
Tennessee Valley Authority, Chattannooga, 
TN; John W. Antalovich of Kucera & Asso- 
ciates, Inc.; Mentor, OH; 
Keddal of R. M. Keddal 
Inc., Library, PA. 



and Robert M. 
& Associates, 



APPROACH 



The purpose of this investigation was 
to compare conventional and high-tech- 
nology geodetic surveying systems using a 
survey grid with physical characteristics 
typical of current longwall mine subsi- 
dence study sites. Since continued aber- 
rant surface movement during the study 
would have masked the comparative mea- 
surements, the grid, as shown in fig- 
ure 1, was installed on the Bureau of 
Mines Pittsburgh Research Center (PRC) 
grounds over a stable surface. 

^Engineering geologist. 
^Physical scientist. 
Pittsburgh Research Center, Bureau of 
Mines, Pittsburgh, PA. 



The grid was developed over gently 
rolling, well-drained topography with 
slopes approaching 30 pet and a maximum 
relief of approximately 150 ft (45 m) . 
Figure 2 shows the grid layout on a 
topographic base map. The grid base- 
line, 1,750 ft (533.4 m) long, was ori- 
ented with two perpendicular cross pro- 
files intersecting it at monuments 4+50 
and 14+50. The profile at monument 4+50 
is 1,200 ft (365.8 m) long; the other 
profile is 650 ft (198.1 m) long. This 
configuration is typical of actual subsi- 
dence grids since it allows cross-section 
capability both parallel and perpendicu- 
lar to the direction of mining. The mon- 
uments were spaced every 25 ft (7.62 m) 



1& . "'-?> 




! SW contro 
,, monument 



FIGURE 1. - Aerial photograph of survey grid. 



and consisted of 2-ft (0.6-m) sections of 
No. 5 reinforcement bars driven into the 
ground. Although the center of the grid 
was located in an open field, the ends of 
the baseline and profiles encountered 
thick vegetation. 

Property boundaries forced control mon- 
ument locations much closer to the grid 
than normal, but since the site was not 
being undermined, there was no danger of 



subsidence alteration. The control monu- 
ment coordinates were determined to a 
first-order accuracy horizontally, and to 
a second-order accuracy vertically. 

The results and conclusions of this 
report should be interpreted in light 
of the prerequisites and requirements 
of surveying for this particular 
application. 



MCELHANL^^- 




Scale, ft 

LEGEND 
Surface monument 

— -Il50 — -Topographical contour 
lines, 5-ft intervals 



Paved road 



zr~.z^rAccess road 

Property boundary line 

— Intermittent stream 
□ Surface structures 



FIGURE 2. - Survey grid on topographic base map. 



SURVEY STUDY 



ELECTRONIC DISTANCE 
METER-THEODOLITE-LEVEL SURVEY 

The grid was installed using conven- 
tional optical alignment procedures and 
two different EDM-theodolite systems, a 
Wild Tl-A 3 and a Topcon GTS-2 semitotal 
station, plus a steel tape. All control 
and grid monuments were then surveyed 
with a precision (second-order) Zeiss 
NI-1 level. The field data were hand- 
tabulated. Computations were performed 
on a Radio Shack TRS-80 model 1000 micro- 
computer. The data were later trans- 
formed using global positioning values, 
a Hewlett-Packard HP41CX calculator, and 
a Stevenson Transformation software 
program. 

The EDM-theodolite surveying system and 
equipment are extremely portable, rugged, 
and relatively simple to operate when 
used by a trained engineering surveyor. 
Strict field procedures and data tabu- 
lation (compilation) are required for 
precise work. Since the data are hand- 
tabulated and compiled, the human factor 
can result in error. In fact, an analy- 
sis of the grid data indicates that such 
an error may have occurred. 

The grid was resurveyed with the EDM- 
theodolite after all other survey systems 
had been developed to detect any possible 
monument movements. 

Environmental constraints imposed on 
the EDM-theodolite system are customary 
and standard. Windy, rainy conditions 
cause a variety of problems including 
lens fogging, survey rod movement, and 
hand tabulation errors. The EDM-theodo- 
lite is particularly susceptible to wet 
weather downtime, primarily in an effort 
to protect the system, and to heat turbu- 
lence on bright, clear sunny days. 

SATELLITE-BASED GLOBAL 
POSITIONING SYSTEM (GPS) 

The NAVSTAR GPS is a space-based, 
worldwide, all-weather system designed to 

^Reference to specific products does 
not imply endorsement by the Bureau of 
Mines . 



provide extremely accurate three-dimen- 
sional navigational and/or positioning 
capability. Present plans call for the 
system to be fully operational in 1989 
(J_). 4 The system, at that time, will 
consist of a constellation of 18 active 
space satellites, plus 3 or more passive 
satellites, orbiting approximately 20,000 
km above the earth in 6 different orbital 
planes. When the entire constellation is 
in place, an observer any place on the 
earth will be able to receive signals 
from a minimum of four satellites at any 
time and determine his position instanta- 
neously (2^ . At present , only 6 of the 
18 satellites have been successfully 
placed in orbit. 

The GPS receiver system demonstrated on 
the grid was the Macrometer interferomet- 
ric surveying system, which is capable of 
receiving NAVSTAR satellite signals but 
is not capable of decoding the special 
military "P" and "S" codes. The system 
is advertised as having three-dimensional 
relative positioning capability to 5 mm 
over a 1-km baseline and 5 cm capabil- 
ity over a 10-km baseline with 2 h of re- 
corded data. The system requires two 
or more receivers, one of which must be 
located over a precisely known survey 
control monument, and the other(s) lo- 
cated on unknown monuments or point(s). 
Survey points can be separated by consid- 
erable distances (miles) and do not have 
to be intervisible. 

The GPS survey was performed on July 9 
and 10, 1984. The survey was designed to 
accomplish three objectives: 

1. Establish first-order horizontal 
and vertical control on the grid datum 
and four control monuments. 

2. Establish coordinates on at least 
two randomly selected grid monuments for 
comparison with other survey data. 

3. Perform repeat observations on a 
minimum of three monuments for comparison 
purposes. 



^Underlined numbers in parentheses re- 
fer to items in the list of references at 
the end of this paper. 



Unfortunately, repeat observation data 
were not provided by the contractor, al- 
though four monuments were occupied in 
more than one session. 

The Macrometer Interferometric Survey 
System includes the field unit V-1000 re- 
ceiver, a remote control-display unit, a 
DEC TU-58 tape drive, and an antenna as- 
sembly. The office-based equipment in- 
cludes a P-1000 data processor, computer 
terminal (monitor), disk drive unit, and 
line printer. A unique, proprietary 
software package is provided with the 
system for data analysis. The field sys- 
tem requires power both from a 115-V-ac 
inverter and from high-amperage 12-V-dc 
batteries. The battery system must 



provide constant power to the precision 
clock system and other systems. The en- 
tire system requires 350 W of power. 

Approximately 2-1/2 h of observation 
time is required to secure first-order- 
accuracy data. The observation window, 
therefore, permitted each survey instru- 
ment to occupy two monuments per day 
since they were close enough to permit 
relocation of the receiver "and antennae 
system within 15 to 20 min. The layout 
of the GPS survey is showh^tn figure 3. 

A tripod is centered over the monument 
to be measured, and an optical plummet 
is used to precisely align and level the 
center of the antenna coupler over the 
center of the monument. An acrylic dome 



Castle Shannon 

Coast and Geodetic Survey 

bench mark 




Pittsburgh Research 
Center 



Not to scale 




Bureau of Mines 

Pittsburgh Research 

Center 



LEGEND 
@U.S. route ©State route 
a Bench mark Not to scale 



LEGEND 

— Main traverse 

— Check line 



Datum 
FIGURE 3. - Layout of the GPS survey. 



protects the antennae from rain, dew, or 
frost without affecting the reception 
performance significantly. 

Although the GPS survey control monu- 
ment sites were very carefully selected 
so as to have open sky above a 20° zenith 
angle and within the azimuth range of the 
known satellite observation sectors, a 
loss of data on one control monument was 
reported by the contractor. The data 
loss also reportedly prevented the com- 
putation of individual survey session 
results from which repeat-reading com- 
parisons could have been documented. 
Accordingly, the survey site selection 
process may be the system's primary envi- 
ronmental constraint. If the stystem can 
only be used in open fields, as was the 
case for three of the four subsidence 
grid control monuments, the constraint 
would seriously limit the use of the 
system for establishing subsidence survey 
control. 

The GPS equipment apparently functions 
satisfactorily in rainy weather. Al- 
though light showers occurred during the 
survey, high winds, thundershowers , and 
lightning were not observed. 

The high-amperage requirement of the 
GPS equipment and its sensitivity to tem- 
perature variations may impose a mea- 
sure of environmental constraint. The 
system requires a stable ac power sys- 
tem plus massive batteries for the dc 
requirements. 

AUTOMATIC RECORDING TACHEOMETER SURVEY 

The automatic recording survey instru- 
ment used in measuring the PRC subsid- 
ence grid was a Zeiss Elta 2 electronic 
tacheometer with digital precision theo- 
dolite, electro-optical range finder, mi- 
crocomputer, program module, and record- 
ing unit. The tacheometer was capable of 
computing, processing, and storing the x, 
y, and z coordinates of the monuments 
instantaneously as they were being mea- 
sured, either in metric, feet, or survey 
"chains" format. Additionally, the ze- 
nith angle, slope distance, and hori- 
zontal azimuth could be recorded or com- 
puted into horizontal distance, direc- 
tion, and difference in elevation and 



then recorded. The smallest range finder 
display unit is 1 mm. Distances of up to 
5 km can reportedly be measured in one 
shot . 

Data acquired and computed in the field 
over the grid during the daytime were 
printed out in easting, northing, and 
elevation format within 1 h after col- 
lection. The tacheometer survey was per- 
formed July 24 and 25, 1984. 

All of the raw data acquired during the 
survey were collected in an arbitrary 
"relative" positioning format. Since 
horizontal and vertical controls were not 
available at the time of the tacheometer 
survey, angular and vertical assumptions 
had to be made. Survey data transforma- 
tion was later performed on the collected 
data using first-order GPS-acquired co- 
ordinates for two control monuments. 

The data were transformed using a sur- 
vey data transformation software package 
on a Hewlett Packard 9845B computer sys- 
tem, HP9885 flexible disk drives, and an 
HP2631B printer. 

Owing to scheduling obligations, the 
tacheometer survey had to be terminated 
abruptly on the second day before a sur- 
vey closure could be completed back to 
the point of origin. Had closure been 
completed, errors could have been spread 
out through the data points using compu- 
tational procedures, rendering the final 
data slightly more precise than those 
contained in this comparative analysis. 
Another control monument was surveyed by 
the tacheometer as the last point mea- 
sured in the lengthy traverse. 

For a short period at the beginning of 
the survey, there were two reflector rod- 
men. Using two rodraen, the instrument 
operator was able to survey seven or 
eight monuments every 3 min. This rate 
includes instrument positioning on the 
reflectors and a rodman positioning on 
monuments in an open field. 

The tacheometer system used had essen- 
tially the same environmental constraints 
as the EDM-theodolite, discussed previ- 
ously. The system was repeatable and 
easy to operate when used by an experi- 
enced surveyor trained on the system. 
Since the system contains a sophisticated 
computer system, function setting, system 



programming, and calibration are more in- 
volved than for conventional systems. 
The basic operational procedures, how- 
ever, were straightforward, easily under- 
stood, and well labeled on the instru- 
ment. A person with basic surveying 
knowledge could produce accurate data 
with a minimum of instruction and train- 
ing. The time required to survey the en- 
tire subsidence grid, consisting of 145 
monuments plus the instrument traverse 
points, with 1 instrument operator and 
1 rodman was approximately 14 h. Since 
each instrument move and/or setup in 
traverse mode requires precise leveling 
and adjustment, the selection of traverse 
instrument station locations is very im- 
portant. Good selection of traverse sta- 
tions for maximum grid monument visibil- 
ity can result in rapid advancement of 
the survey. Poor traverse station selec- 
tion can result in survey time increases. 
Data processing was performed immediately 
after data collection. 

The important factor to consider when 
using the tacheometer is that human error 
involved in the computation is reduced 
essentially to zero. Hand tabulations or 
computations are not performed. Field 
errors can only be made if the instrument 
operator incorrectly sets a function or 
incorrectly tags a data point; in this 
case compiled data will be printed cor- 
rectly but will be incorrectly labeled. 
One such error was made and easily 
detected. 

On extremely clear, bright, hot, sunny 
days, the process of setting up, adjust- 
ing, leveling the instrument, and making 
readings across bright reflective sur- 
faces was considerably more difficult and 
time consuming than on overcast cool 
days. These factors may be the most ser- 
ious environmental constraints and are 
characteristic of laser surveying equip- 
ment. Other constraints that customarily 
apply to surveying equipment relate to 
the use of the system in windy, rainy 
weather. 

AERIAL PHOTOGRAMMETRY SURVEY 

Photogrammetry is frequently employed 
as a precise, noncontact measuring method 



in geotechnical engineering and mining, 
particularly for measuring ground dis- 
placements such as subsidence. 

Conventional survey methods commonly 
take days to gather data. Since subsi- 
dence is a dynamic phenomenon, during 
active periods it is possible to miss 
significant pieces of information by mon- 
itoring the surface as if it were static. 
Photogrammetric surveying eliminates this 
problem because all data are simultane- 
ously recorded on photographs. The ac- 
tual measurement process takes a certain 
amount of time, but since all the work is 
done on photographs, the surface condi- 
tions are frozen in time and the monument 
positions are computed for the instant of 
the photograph. 

Photogrammetry offers two other advan- 
tages over conventional surveys under 
certain conditions. First, a survey can 
be conducted in remote, inaccessible 
areas without significant additional 
cost. However, a ground survey might be 
required to establish a few control 
points outside the subsidence area if no 
existing control data are available. 

Second, the survey will provide much 
greater detail of the visible surface 
area. This offers two valuable options: 
the interpreter may use any visible, dis- 
crete natural object as a monitoring 
point whether originally planned or not; 
and the interpreter may utilize the tech- 
niques of remote sensing to determine the 
effects of subsidence on vegetation or 
other facets of the surface environment. 
This is possible because once the pho- 
tographs exist, they can be reevalu- 
ated, remeasured, and checked for new 
information (3) . 

The survey was conducted on July 31, 
1984. The plane was equipped with a Wild 
model RC-8 camera fitted with a 6-in- 
focal-length lens. To make the 1/2-in- 
diam rebar grid monuments visible from 
the air, reflective 13-in-diam disposable 
aluminum pans were installed over each 
monument. To make the photogrammetric 
analysis more accurate, the distance be- 
tween the top of the rebar monument and 
its marker was measured and recorded for 
adjusting the elevations. 



Aerial photographs were taken at 1,200, 
3,000, and 6,000 ft. Photogrammetric 
analysis, however, was performed only 
on the 1,200-f t-elevation stereo photo- 
graphs. The targets were observable on 
the 3,000- and 6, 000-f t-elevation photo- 
graphs but could not be measured to the 
same accuracy. 

The analysis of the aerial photography 
was performed on a first-order-accuracy 
Matra Traster stereo plotter. The in- 
strument has a reported 1-ym interpreta- 
tion accuracy in both horizontal and 
vertical directions. The system was in- 
terfaced with a Data General model 5/130 
Eclipse computer. Coordinates for each 
target were read three distinct times 
using the system floating mark. The 
computer converts the Traster machine 
stage coordinates into precise ground 
coordinates. 

Photo point coordinates can be read off 
stereo (60-pct overlay) photographs using 
a space coordinate system and either me- 
chanically or mathematically intersect- 
ing the coordinate lines. Although me- 
chanical intersection is performed in 
conventional mapping (stereoplotting) , 
mathematical intersection or analytical 
aerotriangulation and/or stereocompila- 
tion can be performed. The analytical 
technique permits data refinement and 
statistical adjustment for extremely ac- 
curate photo point identification. Addi- 
tionally the procedure permits error 
correction in camera calibration, film 
emulsion deformation, camera platen flat- 
ness, tangential lens distortion, atmos- 
pheric refraction, and earth curvature 
(3). 

The primary environmental constraint in 
photogrammetric surveying is the ground 
visibility requirement. Obviously a 
point must be seen in the photograph if 
it is to be surveyed and its position 
computed. This necessitates clearing 
away any ground cover that might obscure 
the target from the air and making the 
target visible. Photogrammetric surveys 
must generally be conducted in early 
spring and late fall when ground cover is 
at a minimum. However, normal subsidence 
monitoring continues through all seasons. 



In addition, photographs must be taken in 
a clear atmosphere and with a proper sun 
angle for exposure. The problem of tar- 
get visibility is probably the limiting 
factor when deciding whether or not pho- 
togrammetry can be used (3) . 

INERTIAL SYSTEM SURVEY 

The technology began in the early 
1970' s when the Department of Defense de- 
classified an older version of an iner- 
tial navigation system used in early 
space ventures and in high-technology 
aircraft. Prototype inertial surveying 
equipment has been greatly improved and 
is now reportedly accurate enough for 
geodetic survey work over large traverses 
in rough terrain. The equipment is nor- 
mally placed in four-wheel-drive surface 
vehicles; however, it can be flown in 
fixed wing or helicopter-type aircraft. 
The system is moved from established con- 
trol points to unknown monuments and re- 
turned to the original control point or 
to a known second control point. The 
electrostatic gyro inertial system used 
was built by Litton. The system had been 
retrofitted with high-precision acceler- 
ometers for use in research and develop- 
ment by the U.S. Army Corps of Engineers 
Topographic Laboratories. The equipment 
permits survey data accumulation with 
only one operator. 

The sources of noise or error can 
be assigned to three major categories: 

(1) accelerometer measurement error, 

(2) platform drift rate, or (3) environ- 
mental effects. Measurement errors asso- 
ciated with the accelerometer are induced 
by thermal or vibration effects during a 
survey traverse. Platform drift rate oc- 
curs because of vibration variations and 
thermal transients. Environmental noise 
includes variations in the earth's grav- 
ity field, temperature variations, and 
other causes (4^ . 

The inertial surveying was conducted 
on October 3 and 4, 1984. Data obtained 
during the survey were erroneous, how- 
ever, owing to system computer malfunc- 
tions. The system could not be repaired 
and was returned. 



10 



System accuracies have been reported to 
be in the range of 0.33 to 0.82 ft for 
horizontal components. Vertical accuracy 
has been reported to range from 0.03 to 
0.39 ft (_5). 

OTHER HIGH-TECHNOLOGY SURVEY METHODS 

A variety of other remote-sensing tech- 
nologies have been used to detect and 
delineate mine subsidence (6). Studies 
conducted in the Northern Anthracite 
Coalfields of Pennsylvania included Earth 
Resources Technology Satellite imagery 
(ERTS-1), side-looking airborne radar 



(SLAR) imagery, and multispectral scanner 
imagery for 11 spectral bands including 
thermal infrared, color, color infrared, 
and black and white photography. The 
multispectral scanning work was conducted 
to observe subsidence-related moisture 
patterns in bare soil areas. The air- 
craft imagery was used in the detection 
of faults, fractures, and other features 
related to subsidence. Since these tech- 
niques are not of sufficient accuracy or 
resolution to be useful for subsidence 
surveys, they will not be discussed fur- 
ther in this report. 



SURVEY DATA ANALYSIS 



Statistical analyses were performed for 
the EDM-theodolite, tacheometer, and pho- 
togrammetric surveys since the values of 
northing, easting, and height data were 
available for a majority of the monu- 
ments. The GPS system data, however, 
were not used because survey data were 
available for only a few select monu- 
ments. The EDM-theodolite data were used 
as the base for comparison because this 
is a most commonly used method for making 
subsidence measurements. 

Since only a limited number of surveys 
were made using each type of system, the 
ultimate question of accuracy cannot be 
addressed as part of this study. How- 
ever, the difference in monument posi- 
tions can be examined. The statistical 
analyses were therefore performed on the 
difference in individual monument posi- 
tions as identified by a survey method as 
compared to the base (EDM-theodolite). 
All statistical parameters were calcu- 
lated using the absolute value of the 
differences. This approach was used be- 
cause the sign of the difference in monu- 
ment position relative to the base were 



not nearly as important as the magnitude 
of the number. Furthermore, if the ac- 
tual difference values are used, they 
tend to mask the real variation in monu- 
ment position. 

Various statistical parameters are 
shown in table 1. For the tacheometer 
survey comparison, the mean and its stan- 
dard deviation of the northing values are 
approximately twice those of the easting 
values. However, for the photogrammetric 
comparison, the mean and its standard 
deviation of the northing and easting 
values are almost identical. While the 
tacheometer ' s mean elevation is 1/4 to 
1/2 that of its horizontal values, the 
photogrammetric mean elevation is approx- 
imately 2 times its horizontal values. 
Furthermore, the photogrammetric eleva- 
tion shows the largest mean and dis- 
persion observed, approximately 4 times 
those of the tacheometer values. The 
total three-dimensional displacement from 
the base for both the tacheometer (0.25 
ft) and photogrammetry (0.24 ft) is al- 
most identical. 



SUMMARY AND DISCUSSION 



A typical longwall mine subsidence sur- 
vey grid was installed over stable ground 
to compare conventional and high-tech- 
nology survey systems. Five systems were 
employed: inertial, GPS, EDM-theodolite, 
tacheometer, and photogrammetry. High- 
lights of the systems follow: 



Inertial - Extremely portable in that 
it can be placed in surface vehicles and 
aircraft. Sources of error include ac- 
celerometer measurement caused by thermal 
effects, platform drift rate caused by 
vibration variations and thermal tran- 
sients, and environmental effects such as 



TABLE 1. - Statistics on the absolute value of the difference 
in measurements 



11 



Statistic 



Northing Easting Vertical 



TACHEOMETER-THEODOLITE 








138.00 

31.58 

.23 

.01 

.22 

.01 

.09 

.51 

.08 

.43 

1.08 

1.00 


138.00 

12.12 

.09 

.01 

.08 

.00 

.06 

.34 

.00 

.34 

1.24 

2.44 


138.00 
6.53 




.05 




.00 




.05 




.00 




.04 




.44 




.00 




.44 
5.83 




52.66 







PHOTOGRAMMETRY-THEODOLITE 





127.00 
12.22 
.10 
.01 
.09 
.00 
.07 
.25 
.00 
.25 
.32 
-.98 


127.00 
10.97 
.09 
.00 
.07 
.00 
.05 
.26 
.00 
.26 
.55 
-.26 


127.00 
25.64 




.20 




.01 




.17 




.03 




.16 




.67 




.00 




.67 




.94 




.22 



variations in the earth's gravitational 
field and temperature variations. Survey 
data could not be used in this study ow- 
ing to computer malfunction. 

GPS - When completed, will be able to 
determine receiver position instantane- 
ously. Constraints are the high amperage 
required to power the field system and 
sensitivity to temperature variations and 
site selection. This system was used to 
accurately determine the position of the 
control monuments, but the expense and 
time required to survey precluded its use 
over the entire grid. 

EDM-theodolite - Portable, rugged, and 
relatively simple to operate. Sensitive 
to windy and/or rainy conditions and sub- 
ject to errors due to hand tabulations 
and computations. Utilized as the base 
for this comparison because it is the 



most commonly used method for making sub- 
sidence measurements. 

Tacheometer - Completely automated for 
rapid recording, computing, and data gen- 
eration. Subject to the same environmen- 
tal constraints as the theodolite system. 

Photogrammetry - Can be used for inac- 
cessible areas. All data are gathered 
simultaneously, providing a permanent 
photographic record that can be reevalu- 
ated. Surveys cannot be conducted dur- 
ing inclement weather, data for control 
points must be available, and targets 
must be visible on the photographs. 

A statistical analysis indicates that 
the three-dimensional displacements from 
the base (EDM-theodolite) were almost 
identical for the tacheometer and 
photogrammetry . 



12 



REFERENCES 



1. Hothem, L. D. , and C. J. Fronczek. 
Report on Test and Demonstration of Mac- 
rometer Model V-1000 Interferometric Sur- 
veyor. Fed. Geod. Control Comm. , Rep. 
15-83-2, May 1983, 36 pp. 

2. Collins, J. A Satellite Solution 
to Surveying. Prof. Surv. , Nov. -Dec. 
1982, pp. 13-17. 

3. Sendlein, L. V., Y. Hasan, C. L. 
Carlson, and K. R. Herbert (eds.). Sur- 
face Mining Environmental Monitoring and 
Reclamation Handbook (U.S. Dep. Energy, 
Asst. Sec. Energy Tech., Off. Coal Min- 
ing, contract DE-AC-2280-ET-14146) . El- 
sevier, 1980, 750 pp. 



4. Huddle, J. R. Theory and Perform- 
ance for Position and Gravity Survey 
With an Inertial System. J. Guidance and 
Control, v. 1, No. 3, May- June 1978, 
pp. 183-188. 

5. Roof, E. F. Inertial Survey Appli- 
cations to Civil Works. U.S. Army Corps 
Eng., Eng. Topog. Lab., ETL-0309, Jan. 
1983, 63 pp. 

6. Earth Satellite Corp. (Washington, 
DC) . Use of Photo Interpretation and 
Geological Data in the Identification of 
Surface Damage and Subsidence. Appalach- 
ian Reg. Comm. Rep. ARC-73-1 1 1-2554, 1973 
(final rep. 1975), 113 pp. 



13 



SHORT-TERM EFFECTS OF LONGWALL MINING ON SHALLOW WATER SOURCES 
By Noel N. Moebs 1 and Timothy M. Barton 2 

ABSTRACT 



The Bureau of Mines monitored surface 
subsidence, water table levels, and 
stream flow above a longwall panel in 
southwestern Pennsylvania, for about 
6 months prior to mining and 12 months 
afterward. Only water levels within 
the boundary of the longwall showed a 



precipitous decline as a result of min- 
ing. Water levels 500 ft or more outside 
the panel rib line were unaffected. No 
evidence of mining effects on the small 
streams or springs located within 1,200 
ft of the panel was detected. 



INTRODUCTION 



Federal regulations controlling sub- 
sidence are intended to ensure that un- 
derground raining is conducted so as to 
protect the health and safety of the pub- 
lic, minimize damage to the environment, 
and protect the rights of landowners 
(1_). 3 These regulations furthermore re- 
quire the applicant for a mining permit 
to "...identify the extent to which the 
proposed underground mining activities 
may proximately result in contamination, 
diminution, or interruption of an under- 
ground or surface source of water within 
the proposed mine plan or adjacent area 
for domestic, agricultural, industrial, 
or other legitimate use" (2^). 

This is not easily accomplished because 
of the lack of documented quantitative 
information regarding the effects of un- 
derground mining on surface or under- 
ground sources of water. Throughout the 
northern Appalachian bituminous coal re- 
gion, numerous instances of springs, 
streams, or domestic wells going dry be- 
cause of underground coal mining have 
been reported, but without documentation 
or allowances for the effect of seasonal 
changes or precipitation. 

Two recent studies, however, have pro- 
vided some urgently needed information on 
the relation between mining and ground 

1 Geologist. 

^Mining engineer. 
Pittsburgh Research Center, Bureau of 
Mines, Pittsburgh, PA. 

•^Underlined numbers in parentheses re- 
fer to items in the list of references at 
the end of this paper. 



water resources. The first study, by 
Owili-Eger (3), was conducted in the 
Dunkard Basin of the northern Appalachian 
bituminous coal region. The effects of 
longwall mining on well yields and water 
quality were assessed, and conclusions 
were reached as follows: 

1. Water levels in aquifers located at 
least 330 ft above the mine horizon usu- 
ally recovered after mining. 

2. There was a general lowering of the 
piezometric levels. 

3. There was no major lasting deteri- 
oration in the quality of ground water 
systems studied. 

In a second study, Hill, Burgdorf, and 
Price (4) monitored the short-term ef- 
fects of longwall mining on ground wa- 
ter aquifers in western Pennsylvania. 
Eleven wells ranging in depth from 75 to 
250 ft were monitored. Some of the gen- 
eral conclusions resulting from this 
study follow: 

1. Only minor water level declines of 
12 to 31 ft occurred in shallow wells 
less than 100 ft in depth. Water levels 
rebounded to near premining levels within 
2 months after the face had passed be- 
neath a well. 

2. Water level declines of 20 to 211 
ft occurred in wells 160 to 250 ft deep. 
The most precipitous water level declines 
occurred during the 2- to 3-week period 
of maximum surface subsidence, when the 
face still was less than 200 ft beyond a 
well. 

3. Water level declines were greater 
over the center of the longwall panel 
than near the edge or bey«ad. 



14 



The diminution or interruption of water 
sources, especially of shallow domestic 
wells, springs, and small streams, has 
occurred largely as a result of room-and- 
pillar mining, which accounts for about 
93 pet of all underground coal produc- 
tion in the Appalachian region. However, 
longwall mining, a more uniform method of 
extraction, is providing an increasing 
portion of underground coal production, 
and interest in environmental effects and 
damage prevention is shifting toward this 
method. 

In rural areas , such as much of the 
northern Appalachian coal region, the de- 
gree of subsidence damage to frame struc- 
tures generally is not as devastating as 
even a temporary loss of water sources, 
especially in farming. While a certain 
amount of water can be hauled for house- 
hold use, the requirements for watering 
farm animals or washing are substantial 
and heavily dependent on a local supply. 
Therefore, it is essential that the ef- 
fects of mining on local water supplies 
can be assessed and general predictive 
guidelines developed. 

Cautions must be exercised, however, in 
applying general conclusions drawn from 
disparate results to specific mining sit- 
uations, for as Waite (_5) admonishes 
"...there really is no such thing as a 
'typical 1 underground coal mine. Indi- 
vidual mines, even in close proximity to 
one another, often exhibit dramatic dif- 
ferences in relation to ground water." 
It is highly probable, also, that no two 
individual water wells, even in close 
proximity, will respond identically to 
mining and subsidence. 

The Bureau of Mines currently is moni- 
toring surface deformations over longwall 
panels as part of a long-range program to 
improve the prediction of longwall sub- 
sidence and ultimately to control damage 
to surface structures. At one longwall 



monitoring site in southwestern Pennsyl- 
vania (fig. 1), where the first longwall 
panel in the area was mined, the Bureau 
also arranged for the measuring of water 
levels in five 6-in-diam wells, each 
drilled to a depth of 150 ft. These 
wells were located along a survey moni- 
toring profile which extends from the 
centerline of the longwall panel, where 
the first well is located (fig. 2), to 
a distance of 1,270 ft outside the rib 
line, where the outermost hole was 
located. 

The purpose of this study was to deter- 
mine the short-term effects of mining the 
longwall panel on the water levels in the 
five wells, which were intended to simu- 
late a fairly typical domestic water well 
in the region. Wells of this depth (150 
ft) penetrate the shallow water table 
aquifer but do not reach any of the deep- 
er confined aquifers. The term "water 
table" is used here to designate the sur- 
face below which the overburden is sat- 
urated. The water table aquifer extends 
from the water table down through the 
saturated zone to the first layer of rel- 
atively impermeable rock that does not 
transmit ground water rapidly enough to 
supply a well or spring. In the Appa- 
lachian region water wells rarely are 
drilled to the several-hundred-foot 
depths where the deeper aquifers occur 
because these aquifers commonly are of 
very low yield and may be highly saline 
in character. 

Weekly measurements were made of water 
levels in the five wells, and weirs were 
installed on three small streams and one 
spring in the vicinity of the longwall 
panel for measuring flow rates. 

The long-term effects of mining, such 
as the postmining recovery of water lev- 
els, will be reported later, along with 
an assessment of the effects of mining an 
adjacent longwall panel. 



ACKNOWLEDGMENTS 



The author is grateful for the coopera- 
tion of EMway Resources Inc., operators 



of the mine, and to landowners 
Tustin and John T. Gaskill. 



Carl E. 



SITE DESCRIPTION 



The study site at which the water 
sources and subsidence were monitored is 



is near Waynesburg, Greene County, PA, 
in the hilly terrain typical of the 



15 



Pittsbur 




gh I 



^^Uniontown 



WEST VIRGINIA 



FIGURE 1. 



20 

_l 



Scale, miles 
Index map. 



1,000 




LEGEND 

{ ) Surface contou 

O Water well 

I Outline of longwall panel 

J Outline of proposed panel 

▼ V- notch weir 
/* Spring 



FIGURE 2. - Surface features and longwall panel. 

Appalachian Plateau province. Land use 
is chiefly for grazing and hay crops; 
very little is wooded. Bedrock at the 
site is overlain by 7 to 11 ft of resid- 
ual soil consisting of clay and weathered 
shale fragments. There is evidence of 



200 



LU 

o 
< 

rr 

CO 



o 
a: 



bJ 

o 



CO 
Q 



400 



600 



800 



i i 



1 [ 



1 T 



OJ 



I 



rn 



SE 



Clay 

Weathered shale 

Clay shale, silt shale 
Claystone 

Clay shale, silt shale 

Sandstone 

Clay shale, silt shale 

Limestone 

Clay shale, silt shale 

Limestone 

Clay shale, silt shale 

Sandstone 
Argillaceous limestone 

Clay shale, silt shale 

Limestone 

Clay shale, silt shale 

Limestone 

Clay shale, silt shale 

Argillaceous limestone 

Sandstone 

Shale 

Sewickley Coalbed 

Limestone 
Pittsburgh Coalbed 



1,000 
FIGURE 3. - Generalized columnar section. 



weathering 
about 50 ft. 
The geolog 
the overbur 
consists of 
shale, clay 
and coal. 
Pittsburgh 
1,000 ft th: 
1° SE. 



in the bedrock to a depth of 

ic character of the strata in 
den is shown in figure 3 and 
interbedded clay shale, silt 
stone, limestone, sandstone, 
Mine overburden above the 
coalbed ranges from 750 to 
ck, and the strata dip about 



16 



SITE MONITORING 



All measurements of surface deforma- 
tions above the longwall panel were con- 
ducted by a local commercial firm fa- 
miliar with the site. These surface 
deformations are summarized in transverse 



profiles (fig. 4), in longitudinal pro- 
files (fig. 5), and as the final sub- 
sidence contours in the vicinity of water 
wells 1-4 (fig. 6). 




800 700 



600 



500 400 



300 



200 100 100 200 300 400 500 600 700 800 900 

DISTANCE FROM CENTERLINE, ft 

FIGURE 4. - Transverse subsidence profiles. 



_ 1,400 
O 1,300 
> 1,200 



1,100 



-Water well profile 



^m&m&mmm&®$2®s&$&m &n 




ipoo 



DATE OF LONGWALL PANEL FACE POSITION 

1983 




800 600 400 200 200 400 600 800 1,000 

DISTANCE FROM WATER WELL PROFILE, ft 



1,200 1,400 1,600 1,800 2,000 



FIGURE 5. - Longitudinal subsidence profiles. 



17 




0.2 



0.5 




-2.0- 



Panel 



-3.0- 



centerline 




Proposed longwall panel~^y 



LEGEND 
®3 Water well 

-2.5 



Subsidence contour, ft 



200 400 



Scale, ft 



FIGURE 6. - Subsidence contours. 



Measurements of water levels in the 
five water wells and flow rates at the 
three weirs and one spring were conducted 
by the Bureau on a weekly schedule as 
nearly as possible. It is recognized 
that, ideally, observations to establish 
premining hydrologic conditions should be 
conducted for a full year to determine 
seasonal variations. This, however, was 
impossible to accomplish at this site, 
and hence observation water well records 
in the vicinity were examined for sea- 
sonal variations. The wells on the site 



were completed as soon as possible, in 
the second quarter of 1982, the water 
levels were allowed to stabilize for sev- 
eral weeks , and regular measurements were 
begun in July 1982. 

Weirs A and B were installed in May 
1982, and weir C in January 1983. Mea- 
surements of the spring overflow were 
initiated in May 1982. This information 
on surface water sources was compiled 
to supplement that obtained from the wa- 
ter wells. 



WELL WATER QUALITY 



Water samples were bailed from each of 
the five water wells at the study site 
prior to mining of the longwall panel. 
These samples were analyzed, and the re- 
sults are shown in table 1. 

The analysis of well water samples col- 
lected about 12 months after mining had 
reached the profile is shown in table 2. 



It is apparent 
and 2 that there 
in overall water 
ing and 1 year 
passed the wate 
well the pH has 
the alkalinity 
amount . The d 



from comparing tables 1 
is no pronounced change 
quality between premin- 
after the longwall face 

r well profile. In each 

increased slightly and 

has decreased a small 

issolved solids changed 



18 



very little; some increased and some de- 
creased slightly. These minor changes 
could be natural variations, or could be 
attributed to a lowered water table, the 
effects of cascading 4 and a fluctua- 
tion in water level, or possibly altered 
channels of flow in the overburden as a 
result of the subsidence process. No 



correlation could be made between water 
quality and the water levels in the 
wells. 

^Cascading is ground water entering a 
water well above the water level in the 
well, indicating a hydraulically unstable 
condition. 



TABLE 1. - Well water analyses, premining 





Well 1 


Well 2 


Well 3 


Well 4 


Well 5 


Analysis, ppm: 

Alkalinity as CaC03 


211 
245 

17 
0.2 
502 
0.4 
0.1 

80 

ND 

1.0 

2 

13 
101 
0.4 
0.5 

6.8 

410 


207 

184 

17 

0.2 

207 

1.2 

0.2 

94 

ND 

1.6 

2 

11 

57 

1.2 

0.2 

7.0 
600 


252 

197 

23 

0.2 

252 

ND 

0.2 

80 

ND 

2.4 

2 

12 

48 

0.4 

0.1 

7.0 
600 


176 

157 

12 

0.2 

176 

ND 

0.1 

43 

ND 

2.5 

2 

21 

62 

0.7 

0.1 

7.4 
350 


218 




101 


Chloride as NaCl 


29 




0.2 




218 




0.7 




0.1 




38 




ND 




4.4 




2 




53 


Sulfate as SO4 


12 




0.7 




0.2 


PH..... 


7.3 

560 



TABLE 2. - Well water analyses, postmining 





Well 1 


Well 2 


Well 3 


Well 4 


Well 5 


Analysis, ppm: 

Alkalinity as CaC03 


161 

195 
20 
ND 

386 
ND 
ND 
88 
ND 

2.1 

ND 

9 

89 

1.3 
ND 

7.9 

440 


164 

155 
25 
ND 

236 
ND 
ND 
62 
ND 

2.2 

ND 

8 

41 

0.2 
ND 

7.4 
440 


162 

155 
25 
ND 

210 
ND 
ND 
50 
ND 

1.7 

ND 

7 

36 

0.2 
ND 

7.4 
390 


166 

176 
33 
ND 

250 
ND 
ND 
36 
ND 

2.5 
ND 
17 
48 

0.2 
ND 

7.5 

440 


193 




117 


Chloride as NaCl 


45 




ND 




256 




ND 




ND 




38 




ND 




1.8 




ND 




41 


Sulfate as SO4 


29 




0.3 




ND 


PH..... 


7.7 
450 



ANALYSIS OF RESULTS 



mat 



19 



Figure 7 illustrates the general situa- 
tion along profile A-A' of figure 2, in- 
cluding the amount of surface subsidence 
and the depression of the water levels 
(water table) that occurred after the 
longwall panel had been completely ex- 
tracted. Figure 8 illustrates the rela- 
tion of well water levels with respect to 
longwall face advance. 

The most pronounced surface effect from 
the mining is the formation of the sub- 
sidence trough with a maximum subsidence 
of 3.4 ft. Analysis of survey data indi- 
cates a 15° angle of major surface defor- 
mation and a 24° angle to the limit of 
detectable surface deformation (commonly 
referred to as the angle of draw) . 

The most pronounced effect of mining 
on the water table aquifer was indi- 
cated by well 1, which went dry, and by 
wells 2 and 3, in which the water levels 
dropped 10 and 25 ft, respectively. It 
is noteworthy that water levels in wells 



4 and 5, located beyond the 24° limit of 
surface deformation, were unaffected by 
the mining. 

The effects of mining, if any, on the 
streams and spring in the vicinity of 
the longwall panel (fig. 2) were not 
detectable over the short term of this 
study, partly because of normal seasonal 
variations. 

Further details on the results of moni- 
toring the wells , streams , and spring are 
discussed in the following sections. 

WATER WELLS 

Well 1 

After remaining fairly stable for a 
month after monitoring began, the water 
level in well 1, located near the center- 
line of the longwall panel (fig. 2), 
began an unexplained rise in late August 
1982 (fig. 9), when the longwall face was 




1,400 



1,200 



1,000 



800 



< 

> 



600- 



400- 



200 



\ I 
\ \ 

V 

\ 

\ 



Surface 



Panel centerline 



"1 1 

Water level prior to 
panel extraction 




Water level after complete^ 
extraction of panel 



// 



Creek 

5 



»>~\\f c* 



i 



I5°angle to limit of major 
surface deformation 



Mined-out 
longwall panel 



•/A 



25°angle to limit of detectable 
surface deformation 



Proposed 



longwall panel 



1,000 



800 r 
co 



600 o 



LLl 

400 g 

■=> 
ao 
or 

LlI 

200 o 



800 600 400 200 200 400 600 800 1,000 1,200 1,400 1,600 1,800 

DISTANCE FROM CENTERLINE, ft 

FIGURE 7. - Subsidence and water well profiles. 



20 



DISTANCE OF FACE FROM 
WATER WELL SECTION, ft 



1,000 
2,000 
3,000 



Surface 




15° angle to limit of 
major surface deformation 



/ / 
/ / 
/ / 
/ / 
/ / 



/ 



-Longwall panel" 



/ 

if 

II 
1/ 



-25° angle to limit of 

detectable surface 

deformation 



500 



Scale, ft 



If 



FIGURE 8. - Relation of water levels to longwall face advance. 



21 




10 20 10 20 10 20 

JULY AUG. SEPT. 

3.77 3.52 2.33 



MONTHLY RAINFALL, in 



1982 



1983 



FIGURE 9. - Graph of water well levels. Significant precipitation during the winter months 
nated as either rain (R) or snow (S). 



1984 

is desig- 



over 1,450 ft away and mining had not yet 
begun. This rise continued for 3 months. 
A similar but less pronounced rise was 
detected in well 3. The rise cannot be 
explained by precipitation, which was be- 
low average for the 3-month period, nor 
can it be attributed to seasonal effects 
because in this region stream and wa- 
ter table levels generally continue to 
decline through October and sometimes 
November. This is because of the high 
evapotranspiration rates prevailing in 
the summer and fall. 

A declining trend began about December 
2, 1982, when the longwall face was 500 
ft from the well. This trend continued 
for 3 months to February 24, when the 
well went dry. At this time the longwall 
face had progressed to 400 ft past the 
well. 

It is worth noting at this point that 
at this study site the first detectable 
surface subsidence commonly occurs when 
the face has approached to within 500 to 
700 ft of a survey monument, and the 
first major surface subsidence, defined 
here as 10 pet of maximum subsidence, oc- 
curred when the face was about 200 ft 
from the monument (fig. 10). These rela- 
tions are a function of the character and 
thickness of the overburden and the 
thickness of the coalbed and vary from 
site to site. 



10-pct 
subsidence 




z.une ui nisi 

r detectable — -\ 
subsidence 

■" 1 



Direction of mining 



200 400 

DISTANCE TO FACE, ft 



600 



800 



FIGURE 10. - Longitudinal subsidence profile. 

At this site, then, both the land sur- 
face and the water table showed the first 
detectable effects of mining when the 
longwall face had approached to within 
500 ft. At 200 ft, 10 pet of maximum 
subsidence had occurred and the water 
level in the well was falling at a rate 
of 1.6 ft/d. 

Well 1 went completely dry on February 
24, 1983, and remained dry for 3 weeks. 
Cascading then occurred, and water lev- 
els rebounded for about 2-1/2 months, 
finally dropping below the well bottom 
and remaining there for the remainder of 
1983. 



22 



Well 2 

The water in well 2, located over the 
chain pillars 440 ft from the longwall 
panel centerline (fig. 2), remained at a 
relatively constant level throughout most 
of the monitoring. Some minor fluctua- 
tions occurred for an interval of 4 
months from January 6, 1983, when the 
longwall face was directly even with the 
well profile, to May 10, 1983, when the 
face had progressed 1,250 ft past the 
well profile (fig. 5). These fluctua- 
tions probably can be attributed to min- 
ing because wells 4 and 5, located much 
farther away from the panel (fig. 7), re- 
mained unchanged for the same interval 
(fig. 8). Also, well 2 lies within the 
15° angle of major deformation where some 
effects were anticipated. 

Well 3 

The water level in well 3, located 320 
ft beyond the rib line of the longwall 
panel (fig. 7) , was unstable throughout 
most of the 17-month interval of monitor- 
ing from July 1982 to December 1983 (fig. 
9). Water levels varied up to 33 ft. 
While no pronounced effects could be at- 
tributed with certainty to mining, 
water levels during the interval of Janu- 
ary 6 to May 10, 1983, were somewhat more 
unstable than at other times. Also, well 
3 was within the 24° angle of detectable 
surface deformation, so that some effects 
were anticipated. 

The low level of June 8 to October 25, 
averaging 110 ft below the surface, can 
be attributed to the summer season ef- 
fects of high evapotranspiration, after 
which the levels recovered to premining 
levels of about 90 ft. 

Wells 4 and 5 

Wells 4 and 5 are located 580 ft and 
1,270 ft, respectively, outside the rib 
line of the longwall panel and 230 ft and 
920 ft, respectively, beyond the 24° lim- 
it of detectable surface subsidence (fig. 
7). 

Neither well showed any detectable sea- 
sonal or mining effects. Water levels 



remained stable 
of monitoring (f 
Precise compar 
study with those 
such as that des 
and Price (4) , s 
theless, general 
ter level depres 
wall mining were 
each site, as fo 



throughout the 17 months 

ig. 9). 

isons of results of this 
of a similar test site, 

cribed by Hill, Burgdorf, 

hould be avoided. None- 
similarities in the wa- 

sion resulting from long- 
noted in three wells at 

Hows: 



Well location 


Water level 
depression, ft 




Bureau 
site 


Other 
site 


Near panel centerline 
Outside panel: 

350 ft 


-150 (dry) 

-21 



NAp 


108-211 
-14 


4,000 ft 


NAp 








NAp Not applicable. 

The comparison of wells near the mar- 
gins of the panels at these sites yielded 
only erratic results. 

STREAMS 

One very small perennial stream flows 
across the longwall panel about 450 ft 
southeast of the monitoring profile A-A 1 
(fig. 2). The stream flow rate was mea- 
sured at two points, weir A and weir B, 
to establish flow rate characteristics 
and to detect the effects of mining. 

The most outstanding features of the 
hydrograph for weir A (fig. 11) are the 
sharp peak flows of February through May 
and November through December 1983, char- 
acteristic of winter and early spring 
seasons when evapotranspiration is low 
and infiltration rates are high. Between 
peak flows a base flow of about 1 gpm was 
measured for mid- June to mid-November 
1983 due to high evapotranspiration. 
While the peak flows of February through 
May 1982 might have obscured any effects 
from mining activity, which brackets that 
interval (fig. 11), similar peaks recur 
in November through December 1983, indi- 
cating the response of the stream to sim- 
ilar episodes of precipitation is about 
the same and the effects of mining must 
be minimal. 



23 



150 - 




-i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r 




l.ilJiu.1 



Jl, t,J J,l ML Jti IvlfflJ ,« iJifflLll 



u 



A 



LlUlAlhiiil 



jM 



10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 

MAY JUNE JULY AUG SEPT OCT. NOV DEC JAN. FEB. MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC JAN FEB 

342 3.34 3.77 3 52 2.33 0.63 3.11 2.58 1.33 1.68 3.47 5.55 6.40 1.98 3.09 4.26 2.51 3.74 3.68 3.95 1.16 1.81 

MONTHLY RAINFALL, in 
1982 1983 1984 

FIGURE 11. - Hydrograph at weirs A and B. R = rain; S = snow. 



-i — i — i — i — i — r 



n — i — i — i — i — i — i — r 



i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r 




Weir C 



-B-tS i i S r Sr _3? 




j 1 



r, t,J JJ MTtit it! kllLi ,«, id it 111 



.► It i 1 



i.lilLAlU . JjiiLiJ 



10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 

MAY JUNE JULY AUG SEPT OCT NOV DEC JAN. FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC JAN FEB 

342 334 3.77 3.52 2.33 0.63 3.11 2.58 1.33 1.68 3.47 5.55 6.40 1.98 3.09 4.26 2.51 3.74 3.68 3.95 1.16 1.81 

MONTHLY RAINFALL, in 

1982 1983 1984 



FIGURE 12. - Hydrograph at weir C and spring. R = rain; S = sno 



w. 



Weir B was located 1,450 ft downstream 
from weir A (fig. 2) and 1,100 ft outside 
the longwall panel rib line. The hydro- 
graph for weir B is similar to that for 
weir A except that the peak flows are 
higher owing to minor augmentation along 
the 1,450-ft course between the two weirs 
and to more extended premining measure- 
ments. As with weir A, it was antici- 
pated that some change in flow rates due 
to mining might be detected; however, the 



only apparent changes are those easily 
attributed to seasonal effects. Thus, to 
date, no loss of flow rate due to mining 
in the source area can be determined at 
either weir A or B. 

Another very small perennial stream 
located 600 ft off the monitoring pro- 
file A-A' and well outside the panel was 
monitored by weir C (fig. 2) for flow 
rate background data. The source area 
seepages that feed this stream probably 



24 



are far enough outside the panel to be 
free from any pronounced subsidence ef- 
fects. This seams to be confirmed by the 
hydrograph (fig. 12), which shows the 
well-established cycle of peak flows dur- 
ing the winter-spring season of high in- 
filtration and the low flow rates of the 
summer-fall season of high evapotranspi- 
ration. No effects of the mining and 
subsidence in the source area could be 
detected. 

SUMMARY AND 

This report has described the short- 
term effects of mining a longwall panel 
on water resources in the immediate 
vicinity. Monitoring of these effects 
continued for about a year after the 
longwall face had passed the profile 
along which surface deformations and the 
water levels in five observation wells 
were measured. Two very small streams 
and a spring located in the vicinity were 
monitored to establish flow rate charac- 
teristics. This study was conducted un- 
der specific conditions existing at the 
site. The findings are not applicable to 
areas having different topography, geol- 
ogy, and hydrology. 

The results of this study, while 
short term only, support the following 
conclusions : 

1. Water levels in a 150-ft-deep well 
located near the centerline of the panel 
began to decline when the longwall face 
had approached within 500 ft of the well. 
The water levels continued to fall, and 



A spring located about 400 ft north- 
east of weir C (fig. 2) was monitored 
to determine the flow rate charac- 
teristics. The hydrograph for this 
spring (fig. 12) is similar to that for 
weir C, but shows somewhat higher peak 
flows and a higher flow during the sum- 
mer season. No subsidence effects were 
detected. 



CONCLUSIONS 

the well went dry about 2 months after 
the face had passed beneath it, at which 
time the face was 550 ft beyond the well. 
A temporary recovery of the water level 
was attributed to cascading, after which 
the well remained dry. 

2. Water levels in two wells, located 
100 and 300 ft outside the rib line of 
the panel, declined some 15 to 30 ft as a 
result of mining but recovered to near 
premining levels about 10 months after 
the longwall face had passed by. 

3. Water wells located more than 500 
ft outside the longwall panel rib line 
showed no detectable change in water lev- 
els as a result of mining. These wells 
also lie beyond the distance at the 
surface subtended by the 24° angle to the 
limit of detectable surface deformation. 

4. No evidence of mining effects on 
the small streams or spring located 
within 1,200 ft of the panel could be 
detected. 



REFERENCES 



1. U.S. Code of Federal Regulations. 
Title 30 — Mineral Resources; Chapter 
VII — Office of Surface Mining Reclamation 
and Enforcement, Department of the In- 
terior; Subchapter K — Permanent Program 
Performance Standards; Part 817 — Under- 
ground Mining Activities; July 1, 1984. 

2. . Title 30 — Mineral Re- 
sources; Chapter VII — Office of Surface 
Mining Reclamation and Enforcement, De- 
partment of the Interior; Subchapter G — 
Permanent Program Performance Standards; 
Part 783 — Underground Mining Permit Ap- 
plications — Minimum Requirements for 
Information on Environmental Resources; 
July 1, 1984. 



3. Owili-Eger, A. S. C. Geohydrologic 
and Hydrogeochemical Impacts of Longwall 
Coal Mining on Local Aquifers. Soc. Min. 
Eng. AIME preprint 83-376, 1983, 16 pp. 

4. Hill, J. C, G. J. Burgdorf, and 
D. R. Price. Effects of Coal Mine Sub- 
sidence on Ground Water Aquifers in 
Northern Appalachia (contract J0199063, 
SMC Martin Inc.). BuMines OFR 142-84, 
1984, 149 pp., NTIS PB 84-236710. 

5. Waite, B. A. Ground Water Monitor- 
ing of Underground Coal Mines. Min. Eng. 
(Littleton, CO), v. 34, 1982, pp. 170- 
171. 



25 



COMPARISON OF THE SUBSIDENCE OVER TWO DIFFERENT LONGWALL PANELS 
By Paul W. Jeran 1 and Timothy M. Barton 2 

ABSTRACT 



The subsidences over two longwall sec- 
tions operating in the northern Appalach- 
ian coal region were monitored. The 
panels differed in dimensions, overburden 
thickness, and coalbed mined. Although 



the final subsidence profiles differed, 
analysis of the data indicates that the 
same process of subsidence operated at 
each panel. 



INTRODUCTION 



Since 1960, when the first longwall 
with powered supports was installed in 
the United States, the use of the long- 
wall system of mining by the coal indus- 
try has grown. In 1984, 21 U.S. coal 
companies were operating 112 longwalls.3 
Eighty-four of these panels were in the 
northern Appalachian coal region, and the 
majority of these were 500 to 600 ft 
wide. In recent years, the trend has 
been to wider panels because of greater 
productivity allowed by changes in 
equipment. 

One consequence of longwall mining is 
the subsidence of the ground surface 
above the panel. The Bureau has for sev- 
eral years monitored selected mining 
sites to obtain reliable and useful data 
on the reaction of the surface to mining. 
The ultimate goal of this work is to de- 
velop a surface subsidence predictive 
methodology based upon mining and geolog- 
ic parameters. 

The magnitude of subsidence of a point 
on the ground surface is proportional to 
the area of influence coincident with the 
zone of total extraction. In relatively 
flat-lying coalbeds the area of influence 
is typically circular in plan view. If 
the area of influence is entirely within 
the zone of extraction, then the maximum 



Geologist. 



^Mining engineer. 
Pittsburgh Research Center, Bureau of 
Mines, Pittsburgh, PA. 

3 Sprouls, M. W. Longwall Census 1984. 
Coal Min. , v. 21, Dec. 1984, pp. 39-53. 



possible subsidence will occur. If less, 
then the subsidence will be some fraction 
of the maximum subsidence. Figure 1 il- 
lustrates in cross-section the three typ- 
ical geometries using a constant angle of 
draw and constant width of panel. The 
radius of the area of influence is depen- 
dent upon the thickness (H) of the over- 
burden. Traditionally, the terms used to 
describe the three geometries are super- 
critical, where the radius of influence 
(RI) is less than half the width (w) of 




FIGURE 1. - Supercritical, critical, and sub- 
critical geometries. 



26 



the panel; critical, where the radius of 
influence is equal to half the width of 
the panel; and subcritical, where the 
half width of the panel exceeds the ra- 
dius of influence. 

The resulting subsidence curves for 
each of these geometries are shown in 
figure 1. The supercritical geometry re- 
sults in a subsidence curve with multiple 
points of maximum subsidence. The criti- 
cal case has one point of maximum subsid- 
ence. The subcritical case has a maximum 
point at the center, but this is less 
than the maximum possible subsidence. By 
inspection only the supercritical subsid- 
ence trough can be identified by its 



multiple points of maximum subsidence. 
The remaining two cannot be differenti- 
ated without additional information be- 
cause we cannot know if the maximum ob- 
served subsidence is the maximum possible 
subsidence. 

Recently a very wide panel (950 ft 
wide) was monitored. The resultant sub- 
sidence exhibited multiple points of max- 
imum subsidence. This differed from the 
subsidence troughs monitored over typical 
width (450 to 600 ft wide) panels which 
have but a single point of maximum sub- 
sidence. This report compares the data 
from this wide panel with data recently 
obtained from a typical width panel. 



DISCUSSION 



The two longwall panels used in this 
report are in the northern Appalachian 
coal region. The typical width panel, 
designated "E," is in southwestern Penn- 
sylvania. It is 630 ft wide by 4,700 ft 
long. It was chosen because the average 
extracted thickness was the same as that 
at the wide panel, the subsidence was 
typical of the standard width panels we 
have monitored, and the data were ob- 
tained in the same manner as at the wide 
panel. The wide panel, designated "K," 
is in north-central West Virginia. This 
panel is 950 ft wide by 2,100 ft long. 

At both panels, surface survey points 
were installed on 25-ft centers across 
two profiles and a centerline. The ini- 
tial surveys were taken prior to mining, 
and the final surveys were taken a month 
after each panel was finished mining. 
Each panel was surveyed several times 
during mining. Figure 2 is a sketch of 
the survey lines relative to the panels. 

Aside from their dimensions, the panels 
differed in coalbed mined and overburden. 
Panel E operated in the Pittsburgh Coal- 
bed and extracted an average thickness of 
6 ft. Panel K removed the same average 
thickness from the Lower Kittanning Coal- 
bed. Figures 3 and 4 show the variation 
in overburden thickness for the center- 
lines and profiles at each of the 
panels. 

Based upon drillers' logs of the core- 
holes drilled in the vicinity of each 



panel, the overburden at each site aver- 
aged about 30 pet resistant strata (i.e., 
sandstones and limestones). Typical of 
Pennsylvanian age sediments, there is 
lateral variation and the range of re- 
sistant rock content is from 10 to 40 pet 
of the total thickness. 



Profile A 



■^\r- 



h 



570' 475' 



Profile B — 



825' 



♦ b Panel E 
<o Centerline 



1,425' 



Profile A 



Panel K 
Centerline - 



200' 



Profile B 



400' 



o 



400' 



o 
o 

GO 



^1 



■-V- 



FIGURE 2. - Subsidence survey lines at panels 
E and K. 



27 



950- — 

900-- 

850-- 

800-- 

750-- 

«- 700-- 

g 650 -- 
Q 

3 600-- 

CD 

UJ 550-- 
O 

500-- 

450-- 

400-- 

350-- 

300-- 



250' 



H r- 



***^^ 



+ 



H h 



1 ■ !****£ 




V. Panel E centerline 



Panel K centerline 




+ 



400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 2,200,2,400 2,600 2,800 3,000 3,200 3,400 

LOCATION, ft 

FIGURE 3. - Overburden thickness at centerlines. 



1,000 
900 
800-- 
700-- 
£ 600-- 



W 500 
CD 400 

rr 

LU 
> 

O 300 



200-- 



1 oo-- 



{vixvA 




•100 



cm 



Width of panel E 



, Panel K, profile A 

IIIIIIIIIITT7 




Panel K, profile B 



Width of panel K 



■1,000 -800 -600 -400 



-200 200 

LOCATION, ft 



400 600 



800 



1.000 



FIGURE 4. - Overburden thickness at profile lines. 



28 



The final subsidence of the centerline 
for each panel is shown in figure 5. 
Subsidence along each centerline was not 
uniform. Part of this variance may be 
attributed to one or more of the follow- 
ing: variation in overburden thickness, 
variation in extracted thickness, or var- 
iation in the lithologic composition of 
the overburden. 

As the position of the face was re- 
corded for each survey date, its position 
relative to each survey point during each 
survey is easily obtained. If the sub- 
sidence of a point at each survey is 
divided by the final measured subsidence 
of that point and these ratios are plot- 
ted against the relative face position, 
then a curve is obtained that shows the 
movement of the point relative to the 
movement of the face. By plotting these 
ratios from all points along the center- 
line for each panel, figure 6 and 7 re- 
sult. These show that, at both panels, 
the surface exhibited some upheaval as 
the face approached some, but not all, of 
the survey points. Downard movement be- 
gan as the face passed beneath each 
point. If the relative position of the 
face is divided by the overburden thick- 
ness at each point, then the response of 
the surface to the face position in terms 
of overburden thickness may be readily 
compared between the two sites. Figures 
8 and 9 clearly show that, at both sites, 
the subsidence process was over 90 pet 
complete when the face had advanced the 
thickness of the overburden beyond the 
corresponding surface point. 

The final subsidence profiles are shown 
in figure 10. Those from panel K exhibit 



a broad flattish trough, indicating 
supercritical geometry. Profiles from 
panel E show the single point of maximum 
subsidence, which does not indicate the 
degree of criticality. Comparing pro- 
files A and B at panel E, profile B, 
having the greater subsidence and thinner 
overburden, is closer to critical geome- 
try than profile A, assuming all other 
factors are equal. At panel K, profile B 
exhibited a lesser magnitude of subsid- 
ence than did profile A. This may have 
resulted from the thinner overburden not 
compacting the gob as much as the thicker 
overburden. Differences in lithology and 
extracted thickness may also have played 
a part. 

Inclinations between survey points were 
computed from the final profile survey 
data (fig. 11). At each panel, the 
greater inclination was created at the 
profile with the thinner overburden. 
Plotting the inclinations from the cen- 
terline data relative to face position as 
a function of overburden thickness (figs. 
12-13) shows that for each panel, the 
maximum inclination occurred when the 
face was about a third the thickness of 
the overburden past the corresponding 
surface point. The maximum inclination 
over panel K exceeded that over panel E, 
which indicates that the potential for 
damage to surface structures is greater 
over thinner overburden. However, it 
should be noted that at both panels the 
maximum inclinations exceeded the limit 
of 15 mm/m established for protection of 
lowest priority surface structures in the 
Silesian coal basin. 






SUMMARY 



Subsidence over two longwall panels of 
different widths (630 and 950 ft) was 
monitored, and the data were compared. 
The subsidence profiles at the wider pan- 
el show the geometry to be supercritical. 
Those at the narrower panel indicate it 
is most likely subcritical. At both pan- 
els, the subsidence process relative to 
face position can be correlated to over- 



burden thickness. Inclinations at both 
panels were in excess of 15 mm/m, and the 
thinner overburden exhibited the greater 
inclinations. In general, the similarity 
of the response of the overburdens to 
mining at each panel indicates that 
though the final subsidence troughs were 
differently shaped, the process of sub- 
sidence at each site was the same. 



29 



-2.4 

-2.6 

-2.8-- 

H -3.0-- 

ul -3.2 

% -3.4 

3.6 + 



UJ 
Q 

to "3.8 



CD 



•4.0 



3 

co _ 4#2 „ 

-4.4-- 
-4.6-- 



•4.8 



Panel E centerline 



A a AAA 




A AAA A aA A 



AAA> 



Panel K centerline 



400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600 2,800 3,000 3,200 3,400 



LOCATION, ft 
FIGURE 5. - Final subsidence for centerlines. 



10- 

0- 

-10- 

-20- 



o 


-30 


CL 




„ 




UJ 
O 


-40 


z 




UJ 




n 




CO 


-bO 


CO 




z> 




CO 


-60 



•70 



-80 



•90 



100 




fttfA-YWWAVfl; 



AAAIAAAAAAAAAA 



1,000 



-500 



1,500 



500 

FACE POSITION, ft 
FIGURE 6. - Percent of final subsidence versus face position at panel E. 



2p00 



30 



■Jt -30 



O 

z 

Ld 
Q 

CO 

00 



CO 




-100 

-1,000 -800 -600 -400 -200 200 400 600 800 1,000 1,200 

FACE POSITION, ft 

FIGURE 7. - Percent of final subsidence versus face position at panel K. 




-100 



AA A A |A A A A A. 



■1 -0 



2-5 



-0-5 0.0 0.5 1-0 1-5 2-0 

FACE POSITION -OVERBURDEN RATIO 
FIGURE 8. - Percent of final subsidence versus face position as a function of over 
burden thickness at panel E. 



3.0 



31 



Ui 

o 



LU 

Q 



Mw^WiffiS^; 



77 "50 




■100 



-1 .0 



-0.5 



2.5 



0.0 0.5 1-0 1.5 2.0 

FACE POSITION-OVERBURDEN RATIO 
FIGURE 9. - Percent of final subsidence versus face position as a function of over- 
burden thickness at panel K. 



3.0 





0.5- 

o.o- 


i 
i 

cm- 


h 


1 1 1 1 1 1 


1 


*♦- 


-0.5- 
-1 .0- 
-1 .5-J 
-2.0- 


■ 


u^m 


* %V AA A ■ 
D A A A A O 

■4a a ■ 

D \ A A D 
H * A * # 


BM^^_A 


III 
o 

z 
w 

Q 
0> 

00 

=> 
</> 


-2.5- 
-3.0- 
-3.5- 
-4.0- 






A A m 
i ^ ^ 

^iT^iiiiiijHig' 


-- 




-4-5- 


i 


KEY 
3 rofile A 


Profile B ^Ur^" 


-- 




-5.0- 


_ Panel E 
Panel K 


A 

a 


A 
■ 


-- 




-5.5- 
-6.0- 
-6.5- 


1- 


1- 


Width of panel E 


—1 1 h- 




Width of panel K 




1 1 1 1 1 1 



-1,000 -800 



-600 



-400 -200 200 

LOCATION, ft 



400 



600 



800 



1.000 



FIGURE 10. - Final subsidence profiles. 



32 



34 

32+ 

30 

28-- 

26-- 

24-- 

22-- 

20-- 

18-- 

16 



. 14-- 

Z 

O 12-- 

I- 

< 10-- 

z 

3 8- 
o 

Z 6-- 

4-- 

2-- 

0- 

-2- 

-4-- 

-6-- 

-8-- 



KEY 




Profile A 


Profile B 


Panel E A 


A / 


Panel K D 


■/- 



•10 

-1,000 



% 



A 
A A 



H A 

A A 

AA. 



A 
A*. 



D 



J" 



A 
AB 
A 



A 









ZA 



cP 



Width of panel E 
Width of panel K 



+ 



+ 



■800 



-600 



-400 



400 



-200 200 

LOCATION, ft 

FIGURE 11. - Inclination across profiles. 



600 



800 



1,000 



16- 
15- 

14-- 

13- 

12- 

1 1-- 

10- 
9-- 
8-- 
7-- 
6- 
5- 
4- 
3- 
2- 



A 
AA 
A 
A A 
A 
AA 
A 
A 

AAA 

A 

AAiWSA 







AA 



AA A 

AA AA 

■HftA^^A AAA 

A_ 
AA A AAA. 

AA AAA 



•1 -0 



-0.5 



-r 



0.0 



2.5 



0.5 1.0 1.5 2.0 

FACE POSITION-OVERBURDEN RATIO 
FIGURE 12. - Inclination versus face position as a function of overburden thick 
ness, centerline panel E. 



3.0 



33 




1 .0 



•0.5 



0.0 



2.5 



0.5 1.0 1.5 2.0 

FACE POSITION-OVERBURDEN RATIO 
FIGURE 13. - Inclination versus face position as a function of overburden thickness, centerline 
panel K. 



3.0 



34 



PRECALCULATION OF SUBSIDENCE OVER LONGWALL PANELS 
IN THE NORTHERN APPALACHIAN COAL REGION 

By Vladimir Adamek 1 and Paul W. Jeran 2 



ABSTRACT 



The specific lithological conditions 
over the Pittsburgh Coalbed, highly re- 
sistive limestone and sandstone units 
with relatively shallow overburden, pre- 
vent the use of any predictive method as 
developed for European conditions. 

This paper describes the development of 
a subsidence precalculation methodology 
suitable to the raining and geological 
conditions in the northern Appalachian 
coal region. 

It has been found that owing to litho- 
logical conditions over the Pittsburgh 
Coalbed, the subsidence coefficient var- 
ies within the area of the subsidence 
trough. This is different from the Euro- 
pean conditions, where the subsidence 
coefficient is considered to be a 
constant. 

The effects of lithology, in the form 
of a variable subsidence coefficient, 



have been separated for each test site 
by introducing a correlation between 
hypothetically homogeneous overburden and 
existing lithological conditions, while 
providing for different mining 
conditions. 

Field data from 11 Bureau longwall pan- 
el studies were used in the regression 
analysis. For each panel the character- 
istics of the variability of the subsid- 
ence coefficient along individual profile 
lines were defined. Regression analysis 
of the subsidence coefficients from all 
test sites on the location relative to 
the edge of the panel has yielded a 
third-degree polynomial equation with a 
coefficient of correlation of 0.9999. 

All sensitivity tests have shown good 
results. 



INTRODUCTION 



The enactments of Surface Mining Con- 
trol and Reclamation Act of 1977 and Pub- 
lic Law 95-87 made it mandatory that mine 
operators, prior to mining, define — 

1. The aerial extent of surface 
movement. 

2. The surface deformations resulting 
from both vertical and horizontal 
movements. 

3. The time dependency of surface 
movements that will be caused by the pro- 
posed mining. 

Since little or no experience in sub- 
sidence prediction existed in this coun- 
try, the methods developed in Europe were 
applied to meet these requirements. It 



T — '• — : '• 

Mining engineer. 

Geologist. 

Pittsburgh Research 

Mines, Pittsburgh, PA. 



Center, Bureau of 



quickly became apparent that none of the 
methods yielded acceptable results. 

The Bureau of Mines began work on a 
project to develop a predictive model for 
subsidence caused by coal mining in this 
country. To date, field subsidence data 
have been collected from 11 longwall test 
sites via in-house monitoring programs. 
Analysis of these data verified the non- 
applicability of the existing methods to 
U.S. conditions. 

The model presented in this paper is 
limited to predicting vertical movements 
over longwall panels and thus far has 
been investigated only for applications 
in the northern Appalachian coal region. 
It requires the operator only to input 
the geometry of the proposed mining and 
therefore can be used without prior 
knowledge or understanding of the sub- 
sidence process. 



■ - IV, 



35 



DEVELOPMENT OF SUBSIDENCE PRECOMPUTATION METHODOLOGY 



Since the coefficient of subsidence and 
the angle of draw are important to the 
understanding of this model, a discussion 
of these follows. 

COEFFICIENT OF SUBSIDENCE 

For critical and supercirtical situa- 
tions, the coefficient of subsidence is 
defined as a ratio 



smax 

a = » 

m 



where smax = maximum subsidence measured 

and m = extracted coal seam 
thickness , 

For subcritial situations 



a = 



smax 
me 



where 



e = the efficiency coefficient of 
the partial area of 
influence. 



Practically, for all existing predic- 
tive methods, subsidence coefficient a is 
considered to be constant within the 
whole area of the subsidence trough. 

The average coefficient of subsidence a 
can be defined as 

- _ VE 
a VS 

VS = volume of the subsidence trough 
VE = volume of the coal extracted. 

For homogeneous overburden, or overbur- 
den behaving homogeneously from the point 
of view of subsidence, the values of a 
and a should be about equal. 

Moderate discrepancies between the val- 
ues of a and a can be caused by insuffi- 
cient compaction of the gob area at the 
edges of the longwall panel, due to the 
resistance of chain pillars. 

ANGLE OF DRAW 

By definition, the angle of draw is 
identified as an angle between the line 



connecting the top edge of a longwall 
panel with the nearest zero-movement 
point on the surface, and a vertical 
dropped from this point. The angle of 
draw serves at leaste two purposes as de- 
scribed below: 

1. The angle of draw serves to delin- 
eate the surface area influenced by un- 
derground mining. The identification of 
a zero-movement point is a rather dif- 
ficult task, depending on overall circum- 
stances. For relatively shallow overbur- 
den and a smooth surface, good results 
are more probable. 

In reality, in many cases, small sur- 
face subsidences (up to 0.2 to 0.3 ft) 
occur far beyond the edge of the panel, 
suggesting an unrealistically large angle 
of draw. These movements may not even be 
directly connected with underground min- 
ing activities, but can be caused by 
ground water movement, sliding, tempera- 
ture changes, etc. 

Therefore, it would be realistic to de- 
fine the limit angle of draw as the angle 
between a vertical line and the line con- 
necting the upper edge of the panel with 
the place on the surface where surface 
deformations do not exceed a certain lim- 
it. An example follows: 



Vertical movement 



S < 0.1 ft 



Inclination I < 2 mm/m 
Horizontal strains E < 1 mm/m 

2. The angle of draw serves as a 
functional parameter for predictive 
methodologies . 

For a majority of predictive methods 
based on influence functions, the angle 
of draw is the functional parameter that, 
together with the underground geometry 
and overburden thickness, defines the 
characteristics of surface deformations. 

For homogeneous overburden or overbur- 
den behaving homogeneously, the concep- 
tion of the angle of draw as a functional 
parameter for predictive methodologies 
based on the principle of the area of the 
influence has been proven valid. 

Individual theories developed on this 
conception (Keinhorst, Bals, Niemczyk, 



36 



Beyer, etc.) differ from each other very 
little, the differences being caused by 
assigning different values of influence 
to individual zones within the whole area 
of influence. Bals ' theory has achieved 
the widest recognition and practical use 
in Europe. Its substance is the defini- 
tion of the efficiency coefficient e. 
(See appendix. ) 

In accordance with Newton's law govern- 
ing the attraction of masses, Bals 



assumes that each differential part of 
mined-out area within the area of influ- 
ence exerts an influence on the surface 
point inversely proportional to its dis- 
tance from it. 

Using the computer algorithm developed 
by the Bureau, it was possible to compute 
and tabulate the values of e for differ- 
ent mining conditions, i.e., underground 
geometry and overburden thickness (table 
1). 



TABLE 1. - Efficiency coefficients (e) for y = 25' 



w/H 




Distance inward from 


edge of 


panel 


as fraction of 


panel 


width 






0.50 


0.45 


0.40 


0.35 


0.30 


0.25 


0.20 


0.15 


0.10 


0.05 


0.00 


0.1 


0.289 


0.289 


0.289 


0.286 


0.286 


0.280 


0.277 


0.268 


0.258 


0.250 


0.237 




.473 


.471 


.468 


.466 


.460 


.449 


.440 


.428 


.415 


.389 


.361 


0.3 


.609 


.609 


.606 


.599 


.590 


.577 


.563 


.542 


.520 


.487 


.439 


0.4 


.722 


.719 


.714 


.706 


.692 


.676 


.654 


.629 


.594 


.554 


.487 


0.5 


.811 


.808 


.801 


.788 


.772 


.749 


.723 


.686 


.643 


.588 


.500 




.879 


.877 


.868 


.853 


.833 


.803 


.765 


.720 


.667 


.600 


.500 


0.7 


.934 


.931 


.919 


.899 


.870 


.833 


.793 


.744 


.686 


.609 


.500 


0.8 


.973 


.969 


.952 


.927 


.896 


.858 


.818 


.765 


.703 


.622 


.500 


0.9 


.998 


.988 


.972 


.949 


.920 


.882 


.841 


.786 


.720 


.633 


.500 


1.0 


1.000 


.999 


.987 


.967 


.939 


.903 


.861 


.804 


.737 


.644 


.500 




1.000 


1.000 


.977 


.982 


.957 


.921 


.879 


.823 


.751 


.656 


.500 


1.2 


1.000 


1.000 


1.000 


.992 


.972 


.939 


.896 


.841 


.765 


.667 


.500 


1.3 


1.000 


1.000 


1.000 


.999 


.983 


.953 


.913 


.855 


.780 


.677 


.500 


1.4 


1.000 


1.000 


1.000 


1.000 


.992 


.966 


.927 


.870 


.793 


.686 


.500 




1.000 


1.000 


1.000 


1.000 


.999 


.977 


.939 


.884 


.804 


.692 


.500 


1.6 


1.000 


1.000 


1.000 


1.000 


1.000 


.986 


.952 


.896 


.818 


.703 


.500 


1.7 


1.000 


1.000 


1.000 


1.000 


1.000 


.987 


.963 


.909 


.828 


.711 


.500 




1.000 


1.000 


1.000 


1.000 


1.000 


.993 


.972 


.920 


.841 


.720 


.500 


1.9 


1.000 


1.000 


1.000 


1.000 


1.000 


.999 


.979 


.929 


.851 


.728 


.500 


2.0 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


.987 


.939 


.861 


.737 


.500 


2.1 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


.992 


.949 


.870 


.744 


.500 


2.2 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


.997 


.957 


.879 


.751 


.500 




1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


.964 


.888 


.758 


.500 


2.4 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


.972 


.896 


.765 


.500 


2.5 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


.978 


.906 


.772 


.500 


2.6 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


.983 


.913 


.780 


.500 


2.7 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


.988 


.920 


.786 


.500 


2.8 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


.992 


.927 


.793 


.500 


2.9 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


.996 


.934 


.799 


.500 


3.0 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


.999 


.939 


.804 


.500 






Distanc 


e outwa 


rd fron 


i edge o 


f panel 


as f ra 


ction o 


f panel 


width 






0.00 


-0.50 


-0.10 


-0.15 


-0.20 


-0.25 


-0.30 


-0.35 


-0.40 


-0.45 


-0.50 


0.1 


0.237 


0.222 


0.213 


0.201 


0.191 


0.184 


0.180 


0.177 


0.171 


0.166 


0.160 




.361 


.332 


.304 


.288 


.274 


.261 


.246 


.234 


.224 


.214 


.203 


0.3 


.439 


.392 


.357 


.331 


.305 


.286 


.263 


.244 


.227 


.209 


.194 


0.4 


.487 


.418 


.375 


.333 


.297 


.263 


.235 


.207 


.182 


.159 


.139 




.500 


.412 


.356 


.308 


.263 


.228 


.196 


.166 


.139 


.116 


.094 


0.6 


.500 


.400 


.333 


.280 


.235 


.196 


.159 


.130 


.104 


.080 


.061 



37 



TABLE 1. - Efficiency coefficients (e) for y = 25° — Continued 



w/H 


Distance outward from edge 


of panel as fraction 


of panel width — Continued 




0.00 


0.05 


0.10 


0.15 


0.20 


0.25 


0.30 


0.35 


0.40 


0.45 


0.50 


0.7 


0.500 


0.391 


0.314 


0.256 


0.207 


0.166 


0.130 


0.099 


0.073 


0.051 


0.033 


0.8 


.500 


.378 


.297 


.235 


.182 


.139 


.104 


.073 


.048 


.028 


.013 


0.9 


.500 


.367 


.280 


.214 


.159 


.116 


.080 


.051 


.028 


.012 


.001 




.500 


.356 


.263 


.196 


.139 


.094 


.061 


.033 


.013 


.001 


.000 


1.1 


.500 


.344 


.249 


.177 


.121 


.077 


.043 


.018 


.003 


.000 


.000 


1.2 


.500 


.333 


.235 


.159 


.104 


.061 


.028 


.008 


.000 


.000 


.000 


1.3 


.500 


.323 


.220 


.145 


.087 


.046 


.017 


.001 


.000 


.000 


.000 


1.4 


.500 


.314 


.207 


.130 


.073 


.033 


.008 


.000 


.000 


.000 


.000 


1.5 


.500 


.308 


.196 


.116 


.061 


.022 


.001 


.000 


.000 


.000 


.000 




.500 


.297 


.182 


.104 


.048 


.013 


.000 


.000 


.000 


.000 


.000 


1.7 


.500 


.289 


.172 


.091 


.037 


.007 


.000 


.000 


.000 


.000 


.000 


1.8 


.500 


.280 


.159 


.080 


.028 


.001 


.000 


.000 


.000 


.000 


.000 


1.9 


.500 


.272 


.149 


.071 


.021 


.000 


.000 


.000 


.000 


.000 


.000 


2.0 


.500 


.263 


.139 


.061 


.013 


.000 


.000 


.000 


.000 


.000 


.000 


2.1 


.500 


.256 


.130 


.051 


.008 


.000 


.000 


.000 


.000 


.000 


.000 


2.2 


.500 


.249 


.121 


.043 


.003 


.000 


.000 


.000 


.000 


.000 


.000 


2.3 


.500 


.242 


.112 


.036 


.000 


.000 


.000 


.000 


.000 


.000 


.000 


2.4 


.500 


.235 


.104 


.028 


.000 


.000 


.000 


.000 


.000 


.000 


.000 


2.5 


.500 


.228 


.094 


.022 


.000 


.000 


.000 


.000 


.000 


.000 


.000 


2.6 


.500 


.220 


.087 


.017 


.000 


.000 


.000 


.000 


.000 


.000 


.000 


2.7 


.500 


.214 


.080 


.012 


.000 


.000 


.000 


.000 


.000 


.000 


.000 




.500 


.207 


.073 


.008 


.000 


.000 


.000 


.000 


.000 


.000 


.000 


2.9 


.500 


.201 


.066 


.004 


.000 


.000 


.000 


.000 


.000 


.000 


.000 


3.0 


.500 


.196 


.061 


.001 


.000 


.000 


.000 


.000 


.000 


.000 


.000 



In general, subisdence of any surface 
point above a longwall panel can be ex- 
pressed as 

s = smax f(x) = m a f(x). 

The function f(x) is a mathematical ex- 
pression that relates to the physical 
setting and depends mainly on the under- 
ground geometry, overburden thickness, 
overburden properties, and relative posi- 
tion of the surface point toward the 
mined-out area. 

The equation s = m a f(x) is theoreti- 
cally valid for any mining and geological 
conditions because of the broad meaning 
and flexibility of f(x). 

In this equation, there are three un- 
known: s, a, and f(x). After acquiring 
a sufficient amount of field data (s), 
there still remain two unknown members in 
the equation, a and f(x). 

By alternately substituting a as a con- 
stant with computed values from field 
measurements 



a = 



smax 
m 



or 



a = 



smax 
me 



and substituting f(x) with different ex- 
isting predictive methodologies, one may 
verify the validity of individual method- 
ologies for U.S. mining and geological 
conditions. 

After analyzing data from 11 test 
sites, it has been found that none of the 
existing predictive methodologies based 
either on influence or profile function 
is applicable to U.S. mining geological 
conditions. The main reason is the ex- 
treme effect of lithology on the subsid- 
ence characteristics, namely highly re- 
sistant layers of limestone and sandstone 
with relatively shallow overburden. Fig- 
ure 1 shows a typical subsidence profile 
as measured over the Pittsburgh Coalbed 
compared with precalculated profiles 
using the above-mentioned methods. 

As a first step in developing a predic- 
tive model, the problem was approached 
by trying to establish the effect of 



38 






"""*^r-=*J— . 1 


.____ 1 1 


1 1 1 1 




^SS^ --^ s 








^KCn^ 


^^ s ~~~~. 




10 


^T 


"Beyer s ~ 


S 




_ Keinhorst — -»>\ 




\^^ Typical subsidence 
*C profile, 


20 




*$X 


*. Pittsburgh Coalbed ~~ 


30 


Bals--" 


\v /Niemczyk *. 






%. 


\ 


u 






■t 


o- 40 


— 


\\ 


\ - 


LU 
O 




\i 


\ 


§ 50 


— 




\ 


Q 






t, » 


CO 

CO 






V \ 


13 60 

co 


— 




\ \ 








70 












80 














90 


— 




100 


1 1 1 


1 1 


i i r^-3^ 



1 ^=F 
S ^'"^-Bals forr=25' 



10 20 30 40 50 60 70 80 90 I00 

WIDTH, pet 

FIGURE 1. - Comparison of measured profile 
with some precalculated profiles for Pittsburgh 
Coalbed. 

lithology on subsidence characteristics 
for each test site and also to define 
relative differences of this effect be- 
tween individual test sites. This cannot 
be done by simple comparison of sub- 
sidence profiles. Different mining con- 
ditions and underground geometry in- 
cluding depth of cover must be taken into 
account. 

The principle of this idea is to es- 
tablish the difference in subsidence 
characteristics between hypothetically 
homogeneous overburden, i.e. , overburden 
without the presence of resistive hard 
rock units, and existing lithological 
conditions. At the same time, one must 
provide for given mining conditions. 

For computation of subsidences for ho- 
mogeneous overburden, Bals ' theory was 
used. Since one cannot define the exact 
value of the angle of draw, the whole 
process of computation for three concepts 
was repeated, namely, for y = 25°, for y 
= 15° , and also for a constant value of 
efficiency coefficient e = 1 for all 
points. 

According to Bals , the subsidence of 
any surface point for homogeneous over- 
burden is 




p-Edge of panel | <™g 



700 



100 200 300 400 500 600 
DISTANCE FROM THE CENTERLINE, ft 
FIGURE 2. - Comparison of measured profile 
with Bals' predictive method. 



si = m a e 5 

with predetermined or estimated constant 
subsidence coefficient a. 

Figure 2 shows precalculated profiles 
by Bals, using the values of the angle of 
draw y = 15° and y = 25° in comparison 
with measured profile. It is evident 
that there is no possibility of obtaining 
reasonable congruency between precalcu- 
lated and measured profiles for any value 
of y as a functional parameter. This 
leads to the conclusion that the concep- 
tion of using the angle of draw as a 
funtional parameter for direct precompu- 
tation of surface deformations is unsat- 
isfactory for conditions where effect of 
lithology is as overwhelming as it is 
over the Pittsburgh Coalbed. 

The specific lithological conditions 
over the Pittsburgh Coalbed, namely high- 
ly resistive limestone and sandstone 
units with relatively shallow overburden, 
prevent the use of any predictive method 
as developed for European conditions. 
Further, it is also justifiable to assume 
that the resistance of interbedded hard 
rock layers is strongest at the edge of 
the panel and diminishes toward the 
centerline. 

Such a situation must lead to variabil- 
ity of the subsidence coefficient along 
the profile, otherwise considered to be 
constant for homogeneous overburden. 
This assumption is further supported by 
the discrepancy between the subsidence 
coefficient 



asaaffi 



39 



a = 



smax 
m 



or 



a = 



smax 
me 



and the average subsidence coefficient 



VS 
a = VE 



As mentioned before, for homogeneous 
overburden these two values should be 
about equal. 

As shown in table 2, the values of a at 
the centerline of the panel, at each test 
site, are close to 0.6 and a is about 
0.35. Such discrepancy must have a de- 
cisive effect on the subsidence charac- 
teristics. 

To obtain the congruency between pre- 
computed and measured data, the subsid- 



ence coefficient 
variable: 



a w was introduced as a 



sF 
me 



I, 



where SF. = measured subsidence. 



For each surface point at all test 
sites the value of a v ; has been defined. 
Figures 3-8 show the characteristics of 
a v for y = 25° and y = 15° and for con- 
stant e = 1 along all profiles. 

If the assumption about the validity of 
Bals ' theory for homogeneous overburden 
is correct — and no reason has been found 
to doubt it — then each of these curves 
represents a lithological effect on sub- 
sidence characteristics, expressed in the 
form of the variable subsidence coeffi- 
cient. The dispersion of individual 
curves shows the differences of litholog- 
ical effect between individual test 
sites. 

The usefulness of this approach for 
subsidence precalculation depends on two 
possibilities: 

1. The lithological effect on subsid- 
ence characteristics differs at each site 
beyond acceptable limits, as would be 
demonstrated by a large dispersion of in- 
dividual curves. 

2. The lithological effect at each 
site is acceptably similar. Then the 



TABLE 2. - Overview of basic parameters at various test sites 





H 


, ft 


m, ft 


w, ft 


s F at 
centerline, 


a at 
centerline 


a 
(VS/VE) 


w 


Mine 


Range 


At 


H 






centerline 






ft 


for y = 25° 






1 


520-706 


650 


5.5 


460 


-2.62 


0.513 


0.30 


0.71 


2 


677-700 


700 


5.5 


600 


-3.25 


.597 


.35 


.86 


3 


645-700 


700 


5.5 


600 


-3.25 


.597 


.32 


.86 


4 


509-624 


615 


5.5 


605 


-3.65 


.664 


.44 


.98 


5 


652-781 


652 


5.5 


605 


-3.55 


.645 


.39 


.93 


6 


740-795 


795 


5.5 


600 


-3.09 


.587 


.32 


.75 


7 


732-795 


795 


5.5 


600 


-3.09 


.587 


.32 


.75 


8 


913-995 


913 


6.0 


630 


-3.42 


.614 


.40 


.69 


9 


803-913 


913 


6.0 


630 


-3.42 


.614 


.38 


.69 


10 


802-855 


855 


6.0 


630 


-3.12 


.547 


.34 


.74 


11 


717-780 


717 


6.0 


630 


-3.72 


.623 


.34 


.88 


12 


702-719 


717 


6.0 


630 


-3.72 


.623 


.34 


.88 


13 


368-402 


402 


6.0 


940 


-4.04 


.673 


.37 


2.34 


14 


345-40Z 


402 


6.0 


940 


-4.04 


.673 


.39 


2.34 


15 


700-845 


845 


5.5 


600 


-2.95 


.571 


.31 


.71 


16 


747-866 


747 


5.5 


510 


-2.79 


.547 


.34 


.68 



H = Height of th 
m = Effective co 
w = Width of the 
Sr = Subsidences 



e overburden. 

al seam thickness, 

panel, 
measured. 



a = 
a = 
VS = 
VE = 



Subside 
Average 
Volume 
Volume 



nee coeffic 

subsidence 

of the subs 

of the coal 



lent smax/me. 

coefficient, 
idence trough. 

extracted. 



40 



0.7 



i.s 

h- 
y 

u. 
u. 

UJ 

O 4 

UJ 

o 

UJ 

Q 

CO 
00 

CO • 



GO 
< 

a: 



0L_ 
400 



For r = 25° right 




30 m 
_l 



100 ft 



300 



200 100 

DISTANCE FROM EDGE OF PANEL, ft 

FIGURE 3. - Variable subsidence coefficient for y = 25° right 



-100 



-200 



41 



0.7 



o .5 



UJ 

y 

u. 

o .4 

o 

UJ 

•z. 

UJ 

9 

00 _ 
=> .3 

(J) 

UJ 

_J 

DO 

< 

sr 

§.2 



oi — 

400 



For r=25° left 




/^ 



100 ft 



Scale 



Edge of 
panel 



300 200 100 

DISTANCE FROM EDGE OF PANEL, ft 

FIGURE 4. - Variable subsidence coefficient for y = 25° left. 



-100 



-200 



42 



0.7 



3 .5 

\- 

o 

L_ 
U_ 
UJ 
O 4 

UJ 

o 

LU 

Q 

CD 
00 

3 3 
C/) ° 

LU 
_J 
0Q 
< 

S .2 




400 




200 100 

DISTANCE FROM EDGE OF PANEL, ft 

FIGURE 5. - Variable subsidence coefficient for y = 15° right. 



-200 



BsaasHaja 



»™" 



43 



0.7 



3 5 

h- 
z 

UJ 

y 
u. 

UJ 

o .4 

o 

UJ 

o 

z 

UJ 

q 

CO 

CD 

3 .3 

CO 

UJ 

_J 

CD 
< 

cr 
§.2 




0l_ 
400 



30 m 



100 ft 



Scale 



300 200 100 

DISTANCE FROM EDGE OF PANEL, ft 

FIGURE 6. - Variable subsidence coefficient for y = 15° left. 



-100 -200 



44 



0.7 



For constant e=l right 



> 



LU 

o 

LU 
L_ 

LU 
O 

o 

LU 
O 

-z. 

LU 
Q 

CO 
DQ 

Z> 
CO 

LU 

_l 
CO 

< 

or 



0l— 
400 




300 



200 100 

DISTANCE FROM EDGE OF PANEL, ft 

FIGURE 7. - Variable subsidence coefficient for e = 1 right. 



-100 



-200 



i* bi 



Htwmii i nw t mm i 



45 




300 200 100 -100 

DISTANCE FROM EDGE OF PANEL, ft 

FIGURE 8. - Variable subsidence coefficient for e = 1 left. 



-200 



46 



0.7 



6 V 




100 ft 

Scale 





300 



200 



200 100 -100 

DISTANCE FROM EDGE OF PANEL, ft 

FIGURE 9. - Averaged values of variable sub- 
sidence coefficients. 



standard deviations to the averaged val- 
ues of subsidence coefficients would be 
satisfactory. 

Figure 9 shows averaged values of the 
subsidence coefficient a v for y = 25° and 
y = 15° and for constant value of effi- 
ciency coefficient e = 1 for all points. 

Regression analysis of the subsidence 
coefficients from all sites on the loca- 
tion relative to the edge of the panel 
has yielded a third-degree polynomial 
equation with a coefficient of correla- 
tion of 0.9999. 

For y = 25° 

a u = -3.587 x 1CT 8 X 3 + 1.628 



10-5 X 2 _ 9.io5 x 10 -5 X 



+ 1.359 



10 



-1 



For the points located outwards of the 
edge of the panel, X = 0. 

Then, the subsidence of any point to- 
ward the centerline will be 

s j = me j x a v j 

and outwards si = mej x 0.1359. 

Efficiency coefficients ej are tabu- 
lated in table 1 for different mining 
conditions. Interpolation will be nec- 
cesary, where the ratios 

W _ width of the panel 



where X is the distance in feet from the 
edge of the panel toward the centerline. 



H thickness of the overburden 

distance in feet from 
X = the edge of the panel 

W width of the panel 

do not match the values in the table. 

As an example, given a point located 
100 ft inside the edge of a 600-ft-wide 
panel, calculate the subsidence if the 
overburden is 684 ft thick and extracted 
thickness is 5.5 ft. 

Using table 1, first determine the val- 
ues of w/H and X/W where 

w = width of panel, 

H = thickness of overburden, 

and X = distance inside edge of panel. 

w/H = 600/684 = 0.88 X/w = 100/600 = 0.17 

The closest values in the table are 

x/w 



w/h 



By interpolation, the efficiency coeffi- 
cients for X/w = 0.17 at w/H = 0.8 and 
w/H = 0.9 are calculated: 

((0.818 - 0.765)/5) x 2 + 0.765 = 0.786; 

((0.841 - 0.786)/5) x 2 + 0.786 = 0.808. 





0.20 


0.15 


0.8 


0.818 


0.765 


0.9 


0.841 


0.786 



47 



From these, the efficiency coefficient 
for w/H = 0.88 and X/w = 0.17 can be 
interpolated: 

((0.808 - 0.786)/10) x 8 + 0.786 = 0.803. 

Using the Bals algorithm to compute the 
precise efficiency coefficient for the 
above point, a value of 0.8017 is ob- 
tained. The use of either value in the 
regression equation yields a predicted 
subsidence of 1.12 ft. 



Coefficient a u can be 



defined directly 
point identified 
edge of 



from figure 10 for any 

by the distance in feet from the 

the panel. 

As shown in table 2, the majority of 
the field data on which the analyses are 
based comes from longwall panels with a 
width of about 600 ft or less. Only one 
panel is 940 ft wide. 

To avoid any guesswork, the polynomial 
equation has been developed for points 
with maximum distance 300 ft from the 
edge of the panel or up to the center- 
line, whichever comes first. Only for 
panels much wider than 600 ft and over- 
burdens in excess of 800 ft would subsid- 
ences around the centerline have to be 
adjusted to the shape of the precomputed 
partial profile. 



0.7 




300 



200 1 00 

DISTANCE FROM EDGE OF PANEL, ft 
FIGURE 10. - Variable subsidence coefficient 
for y = 25°. 







The equation s ; = m e f a v for subsid- 
ence precomputation is a combination of 
principles on which both influence and 
profile functions are based. 

Efficiency coefficient e represents the 
principles of influence functions, and a v 
represents the principles of profile 
functions. Such a combination seems to 
be justified by at least two logical 
reasons: 

1. Whatever mining geological condi- 
tions are involved, only a certain mined- 
out area influences the movement of a 
surface point. Coefficient e provides 
for that and also for variable mining 

conditions, namely for — ratio. 

rl 

2. At the same time, geological condi- 
tions vary for different mining areas. 
The introduction of a variable subsidence 
coefficient seems to be the only logical 
solution to the problem for mining areas 
where lithological effect on subsidence 
characteristics is so overwhelming. 

As previously stated, the regression 
analysis of the variable coefficient a v 
has been performed for the angles of draw 
y = 25° and y = 15° and for constant e = 
1. The reason is as follows: 

One cannot define the exact value of 
the angle of draw for hypothetically ho- 
mogeneous overburden, i.e., overburden 
without the presence of highly resistive 
hard rock units. Only by comparing re- 
sults from several conceptions can the 
most appropriate be chosen. 

Table 3 contains the computed values of 
a v along each profile with averaged val- 
ues of a v and standard deviations. 

It must be emphasized that the magni- 
tude of standard deviations to a v only 
cannot determine which conception is the 
best. They are influenced by correspond- 
ing efficiency coefficients, which differ 
for each point and different mining 
conditions. 

For a better understanding, a practical 
case was analyzed, namely the profile for 
No. 2 Mine. The width of the panel is w 
= 600 ft, and the coal seam thickness is 
m = 5.5 ft. 

Table 4 shows, for all three concep- 
tions , the comparison between measured 
and precomputed subsidences and compari- 
son of standard deviations ± a j in feet 



48 



TABLE 3. - Variable subsidence coefficients (a v ) along individual profiles with 
averaged values (a v ) and standard deviations (±0;) 



Mine 



Distance inward, 1 ft 



300 



250 



200 



150 



100 



50 



Edge of 

panel 

(0) 



Distance outward, ' ft 



-50 



-100 



-150 



Y ■ 25- 



1 


NA 


NA 


0.480 


0.410 


0.275 


0.182 


0.135 


0.170 


0.210 


0.240 


2 


0.597 


0.590 


.515 


.370 


.235 


.207 


.068 


.053 


.055 


.075 


3 


.597 


.571 


.475 


.335 


.186 


.106 


.098 


.105 


.110 


.150 


4 


.662 


.655 


.565 


.435 


.308 


.205 


.175 


.295 


.230 


.230 


5 


.645 


.627 


.565 


.440 


.318 


.200 


.135 


.120 


.112 


.124 


6 


.587 


.530 


.445 


.335 


.230 


.155 


.100 


.105 


.112 


.115 


7 


.586 


.564 


.502 


.405 


.315 


.235 


.167 


.190 


.170 


.150 


8 


.600 


.530 


.425 


.335 


.270 


.234 


.245 


.265 


.295 


.320 


9 


.610 


.571 


.487 


.380 


.267 


.200 


.180 


.196 


.225 


.225 


10 


.542 


.505 


.430 


.340 


.245 


.175 


.145 


.153 


.165 


.190 


11 


.610 


.545 


.410 


.285 


.193 


.152 


.145 


.145 


.200 


.300 


12 


.622 


.571 


.445 


.250 


.154 


.150 


.180 


.210 


.248 


.248 


13 


.635 


.600 


.535 


.405 


.255 


.130 


.042 


.015 


NA 


NA 


14 


.660 


.621 


.572 


.432 


.250 


.128 


.100 


.122 


.137 


.300 


15 


.575 


.525 


.450 


.350 


.255 


.152 


.098 


.065 


.065 


.055 


16 


NA 


.540 


.460 


.375 


.265 


.192 


.157 


.135 


.110 


.135 


a v . . . . 


.609 


.570 


.485 


.368 


.251 


.169 


.136 


.147 


.163 


.191 


±0;... 


.033 


.043 


.053 


.054 


.045 


.041 


.050 


.074 


.070 


.083 




Y = 15° 


1 


NA 


NA 


0.438 


0.365 


0.225 


0.128 


0.065 


0.039 


0.021 


0.006 


2 


0.591 


0.576 


.482 


.327 


.189 


.075 


.035 


.016 


.011 


.009 


3 


.591 


.555 


.442 


.293 


.149 


.075 


.049 


.033 


.022 


.018 


4 


.662 


.633 


.547 


.398 


.260 


.128 


.088 


.081 


.043 


.018 


5 


.645 


.613 


.529 


.387 


.253 


.138 


.069 


.039 


.025 


.018 


6 


.562 


.529 


.455 


.344 


.245 


.158 


.084 


.062 


.042 


.020 


7 


.562 


.501 


.407 


.287 


.185 


.108 


.051 


.039 


.027 


.015 


8 


.558 


.487 


.378 


.275 


.203 


.151 


.120 


.093 


.078 


.062 


9 


.566 


.523 


.430 


.315 


.203 


.133 


.089 


.066 


.052 


.045 


10 


.513 


.473 


.387 


.288 


.192 


.117 


.074 


.048 


.037 


.030 


11 


.603 


.529 


.382 


.242 


.153 


.104 


.073 


.046 


.044 


.045 


12 


.617 


.548 


.410 


.213 


.121 


.056 


.049 


.049 


.041 


.040 


13 


.635 


.603 


.537 


.400 


.234 


.101 


.022 


.013 


.006 


.005 


14 


.658 


.620 


.570 


.437 


.253 


.102 


.049 


.025 


.009 


.006 


15 


.537 


.489 


.404 


.296 


.198 


.102 


.048 


.023 


.008 


.005 


16 


NA 


.501 


.440 


.340 


.209 


.126 


.079 


.044 


.025 


.022 


a v . . . . 


.593 


.545 


.452 


.325 


.205 


.113 


.065 


.045 


.031 


.023 


±Oj... 


.046 


.053 


.063 


.061 


.040 


.028 


.024 


.022 


.019 


.017 






Di 


stance ii 


ward, 1 i 


:t 




Edge of 
panel 


Distance outwai 


rd, 1 ft 




300 


250 


200 


150 


100 


50 


-50 


-1( 


)0 
















(0) 









CONSTANT e = 1 



NA 

0.590 

.590 

.665 

.645 



NA 

0.575 

.555 

.640 

.612 



0.435 
.480 
.445 
.555 
.526 



0.365 
.330 
.300 
.405 
.393 



0.240 
.210 
.166 
.285 
.281 



0.165 
.095 
.096 
.170 
.180 



0.120 
.068 
.098 
.169 
.131 



0.400 
.070 
.145 
.525 
.152 



0.690 
.110 
.235 
.700 
.190 



NA Not applicable. 



From edge of panel. 



49 



TABLE 3. - Variable subsidence coefficients (a v ) along individual profiles with 
averaged values (a v ) and standard deviations (±aj ) — Continued 





Distance inward, 1 ft 


Edge of 

panel 

(0) 


Distance outward, 1 ft 


Mine 


300 


250 


200 


150 


100 


50 


-50 


-100 









CONSTANT 


e = 1 — Continued 






6 


0.562 


0.500 


0.410 


0.298 


0.207 


0.142 


0.103 


0.195 


0.285 


7 


.565 


.530 


.465 


.365 


.280 


.216 


.168 


.310 


.430 


8 


.560 


.486 


.385 


.300 


.245 


.213 


.247 


.320 


.440 


9 


.570 


.525 


.440 


.340 


.240 


.185 


.185 


.250 


.325 


10 


.505 


.445 


.365 


.277 


.200 


.150 


.163 


.215 


.360 


11 


.607 


.535 


.385 


.256 


.175 


.140 


.153 


.189 


.400 


12 


.620 


.550 


.415 


.220 


.135 


.140 


.180 


.325 


.480 


13 


.632 


.600 


.535 


.400 


.232 


.112 


.038 


.030 


.030 


14 


.660 


.620 


.575 


.440 


.255 


.135 


.100 


.120 


.140 


15 


.535 


.481 


.396 


.305 


.220 


.135 


.098 


.083 


.067 


16 


NA 


.500 


.430 


.335 


.238 


.170 


.155 


.165 


.180 


a v 


.593 


.544 


.453 


.333 


.226 


.153 


.136 


.218 


.316 


±0;... 


.047 


.057 


.065 


.059 


.042 


.036 


.052 


.131 


.202 



NA Not applicable. 



'From edge of panel. 



for a given case. The distribution of 0\ 
(ft) = mejOj for each conception is the 
decisive factor for their evaluation. It 
shows which conception reflects best the 
reality in situ. Despite the relatively 
small differences between a (ft) , the 
conception for y = 25° clearly shows the 
best results. 

Small differences between individual 
conceptions are due to the nature of the 
data from which they were derived. As 
shown on table 2, the range of differ- 
ences between mining conditions (width of 
the panels, overburden thickness) at in- 
dividual test sites is relatively small. 
It means that for mining conditions simi- 
lar to those at the test sites, all three 
conceptions could be used for subsidence 
precomputation with good results. The 
question remains, which one would yield 
the best results, should it be used for 
precomputation at a site with substan- 
tially different mining conditions? For 
example, let us assume that we have to 
precompute subsidences over a longwall 
panel 350 ft wide with 1,800 ft of over- 
burden and coal seam thickness of 6 ft. 
The results are shown on figure 11. The 
difference between individual conceptions 
is obvious. 

From the logical point of view, the 
conception for constant e = 1 is out of 



competition, since it virtually neglects 
different mining conditions and the mag- 
nitude of maximum subsidence becomes only 
a function of the width of the panel. 
More difficult is the choice between the 
conceptions y = 15° and y = 25°. The 
question can be answered only after 
having sufficient field data. 

From available data the conception of y 
= 25° shows the best results. Therefore, 
this conception is considered as the most 
applicable. 



■200 



DISTANCE FROM EDGE OF PANEL, ft 
-100 100 175 100 -100 -200 




Longwall panel 



FIGURE 11. - Precompiled subsidence profiles 
for y = 25° and y = 15° for e = 1. (H = 1,800 ft, 
w = 350 ft). 



50 



TABLE 4. - Comparison of precomputed values for y = 25°, y = 15°, and e = 1 







Distance inwards, 2 


ft 




Edge of 

panel 

(0) 


Distance outward, 2 


Values ' 


300 


250 


200 


150 


100 


50 


ft 




-50 -100 -150 













y = 


25° 












a v . • • • < 


• ••••• 


0.606 


0.567 


0.485 


0.368 


0.251 


0.169 


0.136 


0.146 


0.163 


0.190 


±0,... 


»•••••• 


.032 


.042 


.053 


.054 


.045 


.041 


.055 


.074 


.070 


.083 


e i 


• ••••• 


.990 


.971 


.933 


.878 


.802 


.692 


.500 


.309 


.198 


.121 


a,ej.. 


>•••••• 


.032 


.041 


.049 


.047 


.036 


.028 


.027 


.022 


.014 


.010 


±o,... 


...ft.. 


.18 


.22 


.27 


.26 


.20 


.16 


.15 


.13 


.08 


.060 


sF 


...ft.. 


3.25 


3.17 


2.65 


1.80 


1.04 


.41 


.19 


.09 


.06 


.050 


sP 


...ft.. 


3.30 


3.04 


2.47 


1.77 


1.12 


.64 


.37 


.23 


.15 


.090 


±Aj... 


...ft.. 


.05 


-.13 


-.18 


-.03 


.08 


.23 


.18 


.14 


.09 


.040 













Y = 


15° 












a^. ..•••) 


• • • • 


0.588 


0.540 


0.453 


0.333 


0.226 


0.153 


0.136 


0.218 


0.316 


NA 


±°i 


• • • • 


.046 


.057 


.065 


.059 


.042 


.036 


.052 


.131 


.202 


NA 


fc- j • •»••*> 4 


• • • • 


1.0 


1.0 


1.0 


.976 


.899 


.766 


.5 


.235 


.101 


NA 


tfiej 


• • • • 


.046 


.057 


.065 


.058 


.038 


.038 


.026 


.03 


.02 


NA 


**! 


ft.. 


.25 


.31 


.36 


.32 


.21 


.16 


.14 


.17 


.11 


NA 


sF 


.ft.. 


3.25 


3.17 


2.65 


1.80 


1.04 


.41 


.19 


.09 


.06 


NA 


sP 


ft.. 


3.24 


2.97 


2.49 


1.78 


1.11 


.64 


.37 


.28 


.18 


NA 


±Ai 


ft.. 


-.01 


-.20 


-.16 


-.02 


.05 


.17 


.18 


.19 


.12 


NA 






CONSTANT e = 1 


a v ..... al 


• • • • 


0.587 


0.545 


0.452 


0.325 


0.205 


0.113 


0.065 


0.045 


0.031 


0.023 


±*l 


t m m • ■ 


.05 


.053 


.063 


.061 


.04 


.028 


.024 


.022 


.019 


.017 


±<7j 


.ft.. 


.28 


.29 


.35 


.34 


.22 


.15 


.13 


.12 


.1 


.09 


sF 


.ft.. 


3.25 


3.17 


2.65 


1.80 


1.04 


.41 


.19 


.09 


.06 


.05 


sP 


.ft.. 


3.23 


3. 


2.49 


1.79 


1.13 


.62 


.36 


.25 


.17 


.13 


±Aj 


.ft.. 


-.02 


-.17 


-.16 


-.01 


.09 


.21 


.17 


.16 


.11 


.08 



NA Not applicable. 
Nomenclature explanations: 

a v = averaged variable subsidence coefficient as computed for individual con- 
ceptions (y = 25°, 15°, e = 1). 

Oj = standard deviations to the averaged values of the subsidence coefficient 
a v for individual conceptions. 

ei = efficiency coefficients. 

Oj (ft) = me j a j . 

sF (ft) = subsidences as measured in the field. 

sP (ft) = precomputed subsidences SP = m.ei avi (inwards) 

SP = m.ei 0.1359 (outwards). 

Ai (ft) = differences between measured and precomputed subsidences. 



From edge of panel. 



51 



SENSITIVITY TESTS 



The subsidences of all 16 half profiles 
from 11 test sites with the total of 189 
surface points involved in the regression 
analysis have been computed using 
the polynomial equation developed for y 
= 25°. 

Figure 12 shows the distribution of de- 
viations between computed and directly 
measured subsidences with regard to the 
distance from the edge of the panel. 
Table 5 shows that for 89 pet of all 
points the deviation is between 0.00 and 
0.29 ft, and for 74 pet it is between 
0.00 and 0.19 ft. 

Such results must be considered sat- 
isfactory, especially if the possible 
sources of these deviations are 
considered: 

1. The effect of lithology on subsid- 
ence characteristics is not absolutely 
the same at all investigated sites. 



TABLE 5. - Summary of the distribution of 
deviations 



Deviations 


Number of 


Pet of 


ft 


points 


total 




81 


43 




57 


31 


.20- .29 


29 


15 




14 


7 




4 


2 


.50- .59 


4 


2 


Total 


189 


100 







2. If the estimate of the extracted 
coalbed thickness is inaccurate, the 
full value of the error affects the 
precalculation. 



TIME COEFFICIENT 



Figures 13 and 14 show characteristics 
of time coefficient, involving the sub- 
sidence process. Ninety-five pet of 
total subsidence ususally occurs within 2 



months of passing of the longwall face. 
Residual subsidences may occur during 
several more months. In no case have 
they lasted for more than 1 year. 



0.6 



3 .4 



< .2 
> 

Ld 
Q 



300 









• 

• 

• 
• 


1 1 

• 
• 

• • 
• 

• 

• • 

# • • • • 

• 
• 


1 

• 
• 

• 
• # 

• 
• 

• 

• 

• • 
• 
• 

• • 

• • 


1 1 

Toward the centerline 


1 1 

Outward 


• 

• 
• • 
•• • 

• 

: • •' ! - • ; 

.. . . 

. • . • . •; 


-•—Edge of panel 

• 

: 

• • 

• ' •• •• .' " - 

:: 

• • 

...» •• • • 

• • .i • •♦• •• 



250 200 



50 



00 



50 



-50 -100 -150 



DISTANCE FROM EDGE OF PANEL, ft 

30 m 



100 ft 



Scale 



FIGURE 12. - Distribution of deviations between computed and measured subsidences. 



52 



LlI 



Q 

CO 
CO 

CO 







1 00 200 



LONGWALL FACE POSITION, ft 
300 400 500 600 



i-l 



T 



T 



700 3.500 3,600 

— i ^n 




30 m 



100 ft 



V 



15 23 28 
Feb. 1 

1982 1983 

FIGURE 13. - Characteristics of time coefficient. 



1 00 



60 



40 



23 
Nov. 



o 

a. 



x 

o 
E 
co 



80 Z 



UJ 
CJ 

UJ 

a 
co 

CO 
00 



X 

20 < 



CO 
CD 

3 
CO 



100 



- 2 h 

ul 
a 







23 28 

— »-] Nov.f-«— 



LONGWALL FACE POSITION, ft 
200 300 400 500 600 700 



800 





1 1 1 

pi 


1 1 




-I — - — r 




40- 












~~60^ 


-2 










80- 












cm 


^3 / 








— 


_ Scale / 



1 




30 m 

i 


1 




1 1 


1 


1 1 


Scale 

1 


1 
100 ft 

1 1 



17 



20 



27 



Dec- 



FIGURE 14. 



1984 

Characteristics of time coefficient. 



900 
100 



- 80 



o 
a. 



o 

E 

CO 



UJ 

60 ^ 

LlI 
O 

CO 

m 

z> 

CO 



- 40 



- 20 



x 

< 



3 i 
Jan 
1985 



53 



The extremely low average subsidence coefficient 



a = 



VS 

VE 



Volume of subsidence trough „ 
Volume of the coal extracted 



in comparison with a = 0.6 to 0.8 in Eu- 
ropean conditions may be a cause for some 
concern. It means that about 65 pet of 
the volume of extracted coal has been 
left as underground voids. This is due 
to high resistance of hard rock units, 
decreasing toward the centerline of the 
panel. 



At this time, it is difficult to pre- 
dict whether such a new equilibrium with- 
in the overburden is permanent or not. 
On the test sites that were remeasured 2 
years after mining activities had fin- 
ished, no additional subsidences had 
occurred. 



CONCLUSION 



Good results for subsidence precomputa- 
tion by the developed formula have been 
proven by the sensitivity tests. 

Despite this fact, the methodology must 
be considered to be a preliminary one. 
The regression analysis is based on a 
still limited amount of field data with 
relatively similar mining conditions. 
Its applicability in other mining areas 
has to be tested. The advantages of the 
developed methodology are — 



1. It can be used by persons without 
any previous knowledge of the theory of 
subsidence. 

2. It is relatively simple and fast 
in comparison with existing predictive 
methods. 

3. It eliminates the use of inaccu- 
rately estimated functional parameters 
(maximum subsidence, location of the in- 
flection point, etc.), necessary for ex- 
isting predictive methods. 



BIBLIOGRAPHY 



Adamek, V., and P. W. Jeran. Evalua- 
tion of Existing Predictive Methods for 
Mine Subsidence in the U.S. Paper in 
Proceedings First Conference on Ground 
Control in Mining, ed. by S. S. Peng. 
West Virginia University, July 1981, 
pp. 209-219. 

. Evaluation of Surface Deforma- 
tion Characteristics Over Longwall Panels 
in the Northern Appalachian Coal Field. 
Paper in Proceedings International Sympo- 
sium on Ground Control in Longwall Coal 



Mining and Mining Subsidence - State of 
the Art (Honolulu, Hawaii, 1982). AIME, 
1982, pp. 183-197. 

Bals, R. Beitrag zur Frage der 
Vorausberechnung Bergbaulicher Senkungen 
(Contribution to the Problem of Precalcu- 
lating Mining Subsidence). Mitt, 
aus dem Markscheidewesen 1931/1932, 
pp. 98-111 (in German). 

Niemczyk, 0. Bergschadenkunde (Study 
of Mine Damages). Verlag Gluckauf, 
G.m.b.H., 1949, p. 107 (in German). 



54 



APPENDIX 



To facilitate the use of this precal- 
culation methodology, a basic computer 
program was written for use on a per- 
sonal computer. The program prompts the 
user for the values of point location 
(distance from the edge of the panel in 
feet), overburden thickness, extracted 
coalbed thickness, and width of the 
panel. It then computes the efficiency 
coefficient, e, using an algorithm based 
on Bals 1 theory. This value is used in 
the developed regression equation to cal- 
culate the subsidence of the input point. 
The result is output to the screen. 

Values of the efficiency coefficients e 
cannot be tabulated within the area of H 
tan 25° from the beginning and the end of 
the panel, since within this area there 
are irregular partial areas of influence. 
Therefore, the values of coefficient e 
for surface points within this area have 
to be individually calculated. 

As previously stated, the definition of 
efficiency coefficient e is based on an 
assumption that the extracted area con- 
sists of an infinitely large number of 
small particles i, each of them influ- 
encing the movement of a surface point by 
a force inversely proportional to the 
square of its distance f from it. The 
full area of influence is defined by a 
conical section with its base at the top 
of the coal seam and the apex at surface 
reference point P (fig. A-l). The angle 
of draw y is equal to one half of the in- 
terior angle of the cone. For flat seams, 
the area of influence is a circle. 

Only that part of the full area of in- 
fluence that overlaps the extracted area 
influences the magnitude of displacement 
of investigated point P. 

Based on previously expressed assump- 
tions, the acting force on point P for 
the full area of influence is 

Yl i 

K- / fJTfl. 
YO 



Since f = 



H 



cos y 



(H = overburden thickness) 



Yl 



K=^J cos Yi d Yl . 
Yo 



Surface 




w=600' 

FIGURE A-l. - Graphic definition of subsidence 
by Bals' theory. 



55 



After neglecting — for flat coal seams 
H 2 

and for Yo = to Yi 

K = 1/2 [(sin y cos Y + Y)] ] 



= 1/4 (sin 2yi + 2yi). 

The expression 2y i in the equation is in 
radians. 

Example: For y = 25° and after neglect- 
ing constant factors 1/4 



2.5 



2.0 



K = sin 50° + 50° = 0.766 + 
= 0.766 + 0.872 = 1.638 



50° TT 
360° 



Figure A-2 shows the curve sin 2y + 2y 
for K from y = 0° to 35°. 

To define the coefficient of efficiency e 
for an area that is only a part of the 
full area of influence, Bals' theory di- 
vides the full area into a certain (the- 
oretically unlimited) number of areas of 
equal influence, by annular circles and 
diameters. 

For better understanding and practical 
use, this is demonstrated in the follow- 
ing example (fig. A-l): 

Efficiency coefficient e has to be 
defined for point P. 

Width of the panel w = 600 ft. 

Thickness of the overburden H = 700 ft. 

Angle of draw y = 25°. 

By experience, reasonable accuracy can 
be obtained by dividing the full area of 
influence into 40 sections, by 4 diame- 
ters and 5 concentric circles. Then each 
section bears 2.5 pet of the total influ- 
ence. The influence of section B is 
equal to the influence of the larger but 
more distant section A. 




5 10 15 20 25 30 35 
ANGLE OF DRAW (y), deg 
FIGURE A-2. - The curve sin 2y + ly by Bals. 

First, one must define values of radii 
of single-zone areas: 

For y =25°, the radius of the full 
area is 

r = r 5 = 700' x tan 25° - 700» 

x 0.466 = 326' 

and K = 1.638. 

To obtain single-zone areas of equal 
influence, a particular k must be as- 
signed to each of them. 

For five zones, 



kj = -=- x 1; k2 = 7 x 2; etc. 



For each k, , the corresponding zone 
angle Yj is determined from the curve 
sin 2y + 2y (fig. A-2) : 



Zone 


ki 


Yj, deg 


r j = H tan y 
ft 


» 


1 


0.3276 

.6552 

.9828 

1.3104 

1.6380 


4.6 

9.5 

14.4 

19.5 

25 


56.3 
117.1 
179.7 
247.9 
326 




2 




3 

4 





56 



Each zone area is divided by diame- 
ters into eight sections for better esti- 
mation of extracted area. Parts of sec- 
tions can be measured by planimeter or 
simply estimated: 



Zone 


Sections 




1 

2 
3 
4 
5 


NA 0.3+0.3 NA = 
0.4 + 1.0 + 1.0 + 0.4 = 
.6 + 1.0 + 1.0 + .6 = 
.7 + 1.0 + 1.0 + .7 = 
.8 + 1.0 + 1.0 + .8 = 
Total = 

13.6 x 2.5% = 34% 


0.6 
2.8 
3.2 
3.4 
3.6 
13.6 



Efficiency coefficient e for point P 
is 0.34. For cases that do not require 
high accuracy, single radii of concen- 
tric circles can be determined by divid- 
ing radius of the influence area into 
five equal parts. This method is not 
limited as to the shape of the extraction 
area. 



NA Not applicable. 



#U.S. CPO: 1985-505-019/20,094 



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